Di artikel Matematika kelas 12 ini, kita akan belajar mengenai konsep dasar, rumus, dan cara menghitung teori peluang suatu kejadian. Yuk, simak selengkapnya!
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Wih udah kelas 12 nih, dikit lagi lanjut kuliah. Pasti sekarang kamu lagi mempersiapkan strategi jitu, supaya gak salah pilih kampus dan jurusan impian. Kamu wajib banget untuk cek peluang program studi yang bakal kamu ambil. Nanti, kamu bisa cek lebih lanjut banyaknya daya tampung dan peminat di tahun sebelumnya.
Pokoknya sih, harus jago cari peluang, supaya kamu bisa lolos di kampus impianmu.
Nah, kayak yang udah disinggung sebelumnya tentang peluang. Pas banget nih, di artikel Matematika kelas 12 kali ini, kita mau bahas tentang rumus peluang suatu kejadian. Kamu tau nggak nih, apa yang dimaksud dengan peluang suatu kejadian?
Pengertian Peluang Suatu Kejadian
Singkatnya, peluang suatu kejadian itu adalah kemungkinan dari suatu kejadian. Selain peluang lolos di kampus impian, banyak contoh lain tentang peluang, ya. Bisa peluang mendapatkan bola berwarna merah, peluang menang lomba, peluang turun hujan, dan masih banyak lagi.
Tapi sebelum kita lanjut, ada beberapa hal atau istilah-istilah dasar yang ada di peluang kejadian ini. Jadi, kamu wajib paham karena istilah-istilah ini akan selalu ada di materi peluang.
Baca Juga: Memahami Istilah dalam Peluang: Percobaan, Titik Sampel & Ruang Sampel
Rumus Peluang Suatu Kejadian
Peluang atau kemungkinan, secara teoritis artinya perbandingan antara banyaknya suatu kejadian dengan banyaknya seluruh kemungkinan yang terjadi. Jadi, kita bisa tuliskan rumus peluang kejadian, seperti ini:
Selain rumus peluang suatu kejadian di atas, ada juga sifat-sifat peluang suatu kejadian yang wajib kamu tau. Di antaranya sebagai berikut:
Nah, penting untuk kamu ingat, jika kamu menemukan soal peluang yang memperhatikan urutan/susunannya, misal ada keterangan “diambil berurutan”, maka kamu harus hitung dengan rumus permutasi. Sebaliknya, kalau pada soal disuruh untuk diambil secara acak atau tidak memperhatikan urutan, maka kamu pakai rumus kombinasi.
Hayooo, kamu masih ingat nggak dengan rumus permutasi dan rumus kombinasi? Kalo lupa, coba perhatikan gambar di bawah ini, ya!
Nah, sebelum lanjut ke latihan soal, ada beberapa ringkasan langkah-langkah untuk nentuin hasil peluang suatu kejadian:
- Kamu harus menentukan ruang sampelnya atau n(S) terlebih dahulu.
- Menentukan kejadian peluang atau n(A) yang dikehendaki.
- Terakhir tinggal kamu tentuin peluang nya dengan rumus di atas tadi.
Baca Juga: Yuk, Belajar 5 Jenis Permutasi pada Teori Peluang!
Yuk, langsung aja kita terapkan ke latihan soal!
Cara Menghitung Peluang Suatu Kejadian
Empat bola diambil secara acak dari sebuah box yang berisi 15 buah bola. Karena salah penempatan, 3 bola kempis dan tidak bisa digunakan. Peluang terambilnya empat bola yang tidak kempis adalah….
- 0
- 0,23
- 0,36
- 0,42
- 0,46
Pembahasan:
Dari soal diketahui ada 15 bola dan 3 diantaranya kempis. Jadi, sisa 12 bola yang bisa digunakan.
Nah, karena dari soal tidak ada aturan urutan dalam pengambilan bola, jadi rumus yang kita pakai adalah rumus kombinasi.
Cari n(S) terlebih dahulu:
Banyak cara mengambil 4 bola dari 15 bola adalah
Next, kita cari n(A):
Banyak cara mengambil 4 bola dari 12 bola adalah
Jadi, peluang 4 bola yang terambil tidak pecah adalah
Ternyata gampang kan? yang terpenting kamu harus bisa bedain kapan kamu harus pakai rumus permutasi atau kombinasi, biar nggak salah hitung. Supaya lebih paham, di bawah ini ada satu contoh soal lagi, nih. Coba jawab bersama-sama lagi, ya.
Contoh Soal Peluang Suatu Kejadian
Terdapat sebuah kotak yang berisikan 10 buah balon, yang terdiri dari 3 balon merah dan 7 balon kuning. Hitunglah peluang terambil 3 balon kuning sekaligus!
Pembahasan:
Untuk menghitung banyaknya cara pengambilan 3 balon kuning sekaligus dari 7 balon kuning, dapat digunakan rumus kombinasi:
n(A) = 7C3
7C3 = 7! / (7-3)! × 3!
= 7 × 6 × 5 × 4! / 4! × 3 × 2 × 1
= 7 × 6 × 5 × 4! / 4! × 3 × 2 × 1
= 7 × 5 / 1
= 35
Untuk banyaknya cara pengambilan 3 balon dari 10 balon adalah:
n(S) = 10C3
10C3 = 10! / (10-3)! × 3!
= 10 × 9 × 8 × 7! / 7! × 3 × 2 × 1
= 10 × 9 × 8 × 7! / 7! × 3 × 2 × 1
= 720/6
= 120
Lalu, kita hitung peluang terambil 3 balon kuning sekaligus:
P(A) = n(A) / n(S) = 35/120 = 7/24 = 0,29
Jadi, jawaban yang tepat untuk contoh soal peluang acak di atas adalah 0,29.
Baca Juga: Konsep Kejadian Majemuk dalam Teori Peluang Matematika
Pengertian Peluang Komplemen
Di materi peluang kejadian ini, juga ada yang namanya peluang komplemen, simbolnya kayak gini nih Ac. Peluang komplemen sering juga tuh keluar di soal-soal ujian teori peluang. Kalau begitu, apa sih yang dimaksud peluang komplemen? Jadi, peluang komplemen (Ac) adalah peluang semua kejadian yang bukan A.
Rumus Peluang Komplemen
Peluang kejadian punya hubungan dengan peluang komplemen. Dari hubungan itu lah, kita bisa mendapatkan rumus peluang komplemen. Hubungan antara peluang kejadian A dengan komplemennya (Ac), antara lain:
Cara Menghitung Peluang Komplemen
Diketahui suatu kantong berisi 8 bola merah, 4 bola putih, dan 2 bola hijau. Peluang terambilnya bola bukan merah adalah ….
Pembahasan:
Misal: P(A)= peluang terambilnya bola merah
Maka, untuk mencari peluang terambilnya bola merah atau
Yuk kita cari terlebih dahulu P(A) dengan rumus:
n(A) adalah banyaknya bola merah dalam kantong, berarti n(A)= 8
Sedangkan n(S) banyaknya sampel yaitu jumlah semua bola yang ada di kantong,
n(S) = 8 + 4+ 2 = 14.
langsung aja kita substitusi ke rumus:
Baca Juga: Kombinasi dan Binomial Newton dalam Aturan Pencacahan
Contoh Soal Peluang Komplemen
Tiga uang koin dilempar secara bersamaan. Peluang tidak muncul gambar satu pun adalah…
Pembahasan:
Misal: P(A) = peluang munculnya gambar
Maka, untuk mencari peluang tidak muncul gambar adalah P(Ac) = 1 – P(A)
Cari terlebih dahulu P(A) dengan rumus:
P(A) = n(A) / n(S)
n(A) adalah banyaknya gambar yang ada pada ruang sampel, berarti n(A) = 7
Sedangkan n(S) adalah banyaknya sampel, berarti n(S) = 8
Langsung kita substitusi ke rumus:
P(A) = n(A) / n(S) = 7/8
Lalu, kita cari peluang komplemennya:
P(Ac) = 1 – P(A) = 1 – 7/8 = 8/8 – 7/8 = 1/8 = 0,125
Jadi, peluang tidak muncul gambar satu pun adalah 0,125.
Frekuensi Harapan Suatu Kejadian
Ketika kamu belajar peluang kejadian, jangan bingung kalo kamu nemuin frekuensi harapan. Frekuensi harapan atau disimbolkan dengan Fh(A), bisa juga disebut sebagai ekspektasi suatu kejadian.
Kalo suatu percobaan dilakukan berulang kali, maka frekuensi harapan muncul suatu kejadiannya akan semakin besar.
Rumus Frekuensi Harapan Suatu Kejadian
Jadi, frekuensi harapan pada suatu percobaan adalah hasil kali banyaknya percobaan dengan peluang kejadian secara teoritis. Rumus frekuensi harapan bisa ditulis sebagai berikut:
“Biasanya soal frekuensi harapan suatu kejadian kaya gimana sih?”
Nah, langsung masuk ke contoh soal aja yuk!
Cara Menghitung Frekuensi Harapan Suatu Kejadian
Sebuah dadu dilempar 24 kali. Jika A adalah kejadian muncul mata dadu prima ganjil, maka tentukanlah frekuensi harapan munculnya kejadian A!
Pembahasan:
Diketahui dari soal n = 24
Ingat Rumus Frekuensi Harapan:
Nah, karena A adalah mata dadu prima ganjil, maka A={3,5}
atau n(A)= 2.
Untuk S = {1,2,3,4,5,6} maka n(S)= 6
Lanjut, tinggal masukan ke dalam rumus frekuensi harapan.
Jadi, frekuensi harapan kejadian A adalah 8.
Contoh Soal Frekuensi Harapan
Sudah paham teorinya, sekarang kita latihan soal, yuk!
Terdapat 7 buah kartu yang ditulisi huruf A, B, C, D, E, F, G. Lalu, dari kartu tersebut diambil sebuah kartu secara acak. Jika pengambilan dilakukan sebanyak 70 kali dengan pengembalian, maka frekuensi harapan terambil kartu yang bertuliskan huruf vokal adalah…
Pembahasan:
Diketahui:
n(A) = banyaknya huruf vokal yang tersedia yaitu 2 (A dan E)
n(S) = banyaknya kartu yaitu 7
n = banyaknya pengambilan yaitu 70 kali
Maka, frekuensi harapan terambil kartu bertuliskan huruf vokal adalah:
fh(A) = n x P(A)
= n x n(A) / n(S)
= 70 x 2 / 7
= 20
Jadi, frekuensi harapan terambil kartu bertuliskan huruf vokal adalah 20.
Baca Juga: Konsep Dasar Peluang Empiris, Rumus, dan Contoh Soalnya
Wah, lengkap banget nih pembahasan mengenai peluang ini. Kamu sudah belajar banyak mengenai rumus-rumus peluang kejadian, peluang komplemen, frekuensi harapan, disertai contoh soalnya. Ternyata cukup mudah kan, guys?
Sebenarnya materi peluang gak berhenti sampai di sini aja ya, karena masih ada lagi pembahasan yang lebih seru. Aku kasih contohnya nih, ada peluang kejadian yang saling lepas, saling bebas, dan masih banyak lagi! Semua materi ini penting loh!
Makanya jangan sampai kelewatan untuk terus belajar dan bahas-bahas soal di ruangbelajar. Materinya lengkap, pembahasan soal yang terupdate terus-menerus ditambah lagi pembahasan soal nya gampang dipahami, langganan sekarang aja yuk.
Sampai jumpa di artikel berikutnya ya, dadah!
Referensi:
Nugraha, S dan Sulaiman. (2012) Buku Jagoan Matematika SMA/MA Kelas 10,11,12. Depok: Penerbit Pustaka Makmur.
Sutrisno, J. dan Foster, B. (2019) Fokus Belajar Inti Sari Matematika untuk SMP/MTs. Jakarta: Penerbit Duta.
Artikel pertama kali ditulis oleh Tedy Rizkha Heryansyah dan diperbarui pada 29 Juni 2022 oleh Efira Yesika.
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<h1 class="content-title">
Pahami Konsep, Rumus & Cara Menghitung Peluang Suatu Kejadian | Matematika Kelas 12 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kak-efira-mt-saintek" class="">Kak Efira MT Saintek</a> </p>
<p class="content-info"><span>September 28, 2022 • </span> <span>7 minutes read</span></p>
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<p style="text-align: left;"><span style="font-weight: 400;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Peluang%20Suatu%20Kejadian.jpg" alt="Cara Menghitung Peluang Suatu Kejadian" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></p>
<p style="text-align: center;"><span style="color: #000000;"><em>Di artikel Matematika kelas 12 ini, kita akan belajar mengenai konsep dasar, rumus, dan cara menghitung teori peluang suatu kejadian. Yuk, simak selengkapnya!</em><span style="font-weight: 400;"></span></span></p>
<p style="text-align: center;"><span style="color: #000000;">—<span style="font-weight: 400;"></span></span></p>
<p style="text-align: center;"><span style="color: #000000;"><span id="more-1459"></span></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Wih udah kelas 12 nih, dikit lagi lanjut kuliah. Pasti sekarang kamu lagi mempersiapkan strategi jitu, supaya gak salah </span><a href="/blog/tag/kampus-dan-jurusan" rel="noopener" style="font-weight: bold;">pilih kampus dan jurusan impian</a><span style="color: #000000;">. Kamu wajib banget untuk cek peluang program studi yang bakal kamu ambil. Nanti, kamu bisa cek lebih lanjut banyaknya daya tampung dan peminat di tahun sebelumnya.</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Pokoknya sih, harus jago cari peluang, supaya kamu bisa lolos di kampus impianmu.</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, kayak yang udah disinggung sebelumnya tentang peluang. Pas banget nih, di </span><a href="/blog/tag/matematika-xii" rel="noopener" style="font-weight: bold;">artikel Matematika kelas 12</a><span style="color: #000000;"> kali ini, kita mau bahas tentang rumus peluang suatu kejadian. Kamu tau nggak nih, apa yang dimaksud dengan peluang suatu kejadian?</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;">Pengertian Peluang Suatu Kejadian</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Singkatnya, <span style="font-weight: bold;">peluang suatu kejadian itu adalah kemungkinan dari suatu kejadian</span>. Selain peluang lolos di kampus impian, banyak contoh lain tentang peluang, ya. Bisa peluang mendapatkan bola berwarna merah, peluang menang lomba, peluang turun hujan, dan masih banyak lagi.</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Tapi sebelum kita lanjut, ada beberapa hal atau istilah-istilah dasar yang ada di peluang kejadian ini. Jadi, kamu wajib paham</span><span style="color: #000000;"> karena istilah-istilah ini akan selalu ada di materi peluang.</span></p>
<p style="text-align: left;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Istilah%20Peluang%20Kejadian.jpg" alt="Istilah dalam Peluang Suatu Kejadian" width="600" loading="lazy" style="width: 600px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: left;"> </p>
<p style="text-align: justify; font-weight: bold;">Baca Juga: <a href="/blog/materi-peluang-percobaan-ruang-sampel-dan-titik-sampel" rel="noopener">Memahami Istilah dalam Peluang: Percobaan, Titik Sampel & Ruang Sampel</a></p>
<p style="text-align: justify; font-weight: bold;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;"><strong>Rumus Peluang Suatu Kejadian</strong></span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Peluang atau kemungkinan, secara teoritis artinya <strong>perbandingan antara banyaknya suatu kejadian dengan banyaknya seluruh kemungkinan yang terjadi</strong>. Jadi, kita bisa tuliskan rumus peluang kejadian, seperti ini:</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rumus%20Peluang%20Kejadian.jpg" alt="Rumus Peluang Kejadian" width="600" loading="lazy" style="width: 600px; margin-left: auto; margin-right: auto; display: block;"></span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="color: #000000;">Selain rumus peluang suatu kejadian di atas, ada juga sifat-sifat peluang suatu kejadian yang wajib kamu tau. Di antaranya sebagai berikut:</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Sifat-sifat%20peluang%20kejadian.jpg" alt="Sifat-sifat peluang kejadian" width="600" loading="lazy" style="width: 600px; margin-left: auto; margin-right: auto; display: block;"></span></p>
<p style="text-align: justify; font-weight: bold;"> </p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, penting untuk kamu ingat, <span style="font-weight: bold;">jika kamu menemukan soal peluang yang</span><strong> memperhatikan urutan/susunannya, </strong><span style="font-weight: normal;">misal ada keterangan “diambil berurutan”,</span><strong> maka kamu harus hitung dengan rumus permutasi. </strong><span style="font-weight: normal;">Sebaliknya,</span><strong> kalau pada soal disuruh untuk diambil secara acak atau tidak memperhatikan urutan, maka kamu pakai rumus kombinasi.</strong></span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">Hayooo, kamu masih ingat nggak dengan rumus permutasi dan rumus kombinasi? Kalo lupa, coba perhatikan gambar di bawah ini, ya!</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Perbedaan%20Kombinasi%20dan%20Permutasi.jpg" alt="Rumus Kombinasi dan Rumus Permutasi" width="600" loading="lazy" style="width: 600px; margin-left: auto; margin-right: auto; display: block;"></strong></span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, sebelum lanjut ke latihan soal, ada beberapa ringkasan langkah-langkah untuk <em>nentuin</em> hasil peluang suatu kejadian:</span></p>
<ol>
<li aria-level="1"><span style="color: #000000;">Kamu harus menentukan ruang sampelnya atau <em>n(S)</em> terlebih dahulu.</span></li>
<li aria-level="1"><span style="color: #000000;">Menentukan kejadian peluang atau <em>n(A)</em> yang dikehendaki.</span></li>
<li aria-level="1"><span style="color: #000000;">Terakhir tinggal kamu tentuin peluang nya dengan rumus di atas tadi.</span></li>
</ol>
<p style="font-weight: bold;"><span style="color: #000000;">Baca Juga: <a href="/blog/jenis-permutasi-dalam-teori-peluang" rel="noopener">Yuk, Belajar 5 Jenis Permutasi pada Teori Peluang!</a></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Yuk, langsung aja kita terapkan ke latihan soal!</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify;"><span style="font-size: 20px; color: #000000;"><strong>Cara Menghitung Peluang Suatu Kejadian</strong></span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Empat bola diambil secara acak dari sebuah box yang berisi 15 buah bola. Karena salah penempatan, 3 bola kempis dan tidak bisa digunakan. Peluang terambilnya empat bola yang tidak kempis adalah….</span></p>
<ol style="list-style-type: lower-alpha;">
<li aria-level="1"><span style="color: #000000;">0</span></li>
<li aria-level="1"><span style="color: #000000;">0,23</span></li>
<li aria-level="1"><span style="color: #000000;">0,36</span></li>
<li aria-level="1"><span style="color: #000000;">0,42</span></li>
<li aria-level="1"><span style="color: #000000;">0,46</span></li>
</ol>
<p> </p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Pembahasan:</strong></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Dari soal diketahui ada 15 bola dan 3 diantaranya kempis. Jadi, sisa 12 bola yang bisa digunakan. </span></p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, karena dari soal tidak ada aturan urutan dalam pengambilan bola, jadi rumus yang kita pakai adalah <span style="font-weight: bold;">rumus kombinasi</span>.<span style="font-size: 20px;"></span></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Cari n(S) terlebih dahulu:</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Banyak cara mengambil 4 bola dari 15 bola adalah</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-03-54-10-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Next, kita cari n(A):</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Banyak cara mengambil 4 bola dari 12 bola adalah</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-04-18-65-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Jadi, peluang 4 bola yang terambil tidak pecah adalah</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-04-43-00-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Ternyata gampang kan? yang terpenting kamu harus bisa bedain kapan kamu harus pakai rumus permutasi atau kombinasi, biar nggak salah hitung. Supaya lebih paham, di bawah ini ada satu contoh soal lagi, nih. Coba jawab bersama-sama lagi, ya.</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-weight: bold; font-size: 20px;"><span style="color: #000000;">Contoh Soal Peluang Suatu Kejadian</span></h2>
<p style="text-align: justify; font-weight: normal;">Terdapat sebuah kotak yang berisikan 10 buah balon, yang terdiri dari 3 balon merah dan 7 balon kuning. Hitunglah peluang terambil 3 balon kuning sekaligus!</p>
<p style="text-align: justify; font-weight: bold;">Pembahasan:</p>
<p style="text-align: justify; font-weight: normal;">Untuk menghitung banyaknya cara pengambilan 3 balon kuning sekaligus dari 7 balon kuning, dapat digunakan rumus kombinasi:</p>
<p style="text-align: justify; font-weight: normal;">n(A) = <sub>7</sub>C<sub>3</sub></p>
<p style="text-align: justify; font-weight: normal;"><sub>7</sub>C<sub>3</sub> = 7! / (7-3)! × 3!</p>
<p style="text-align: justify; font-weight: normal;"> = 7 × 6 × 5 × 4! / 4! × 3 × 2 × 1</p>
<p style="text-align: justify; font-weight: normal;"> = 7 × <span style="text-decoration: line-through;">6</span> × 5 × <span style="text-decoration: line-through;">4!</span> / <span style="text-decoration: line-through;">4!</span> × <span style="text-decoration: line-through;">3 × 2</span> × 1</p>
<p style="text-align: justify; font-weight: normal;"> = 7 × 5 / 1</p>
<p style="text-align: justify; font-weight: normal;"> = 35</p>
<p style="text-align: justify; font-weight: normal;">Untuk banyaknya cara pengambilan 3 balon dari 10 balon adalah:</p>
<p style="text-align: justify; font-weight: normal;">n(S) = <sub>10</sub>C<sub>3</sub></p>
<p style="text-align: justify; font-weight: normal;"><sub>10</sub>C<sub>3</sub> = 10! / (10-3)! × 3!</p>
<p style="text-align: justify; font-weight: normal;"> = 10 × 9 × 8 × 7! / 7! × 3 × 2 × 1</p>
<p style="text-align: justify; font-weight: normal;"> = 10 × 9 × 8 × <span style="text-decoration: line-through;">7!</span> / <span style="text-decoration: line-through;">7!</span> × 3 × 2 × 1</p>
<p style="text-align: justify; font-weight: normal;"> = 720/6</p>
<p style="text-align: justify; font-weight: normal;"> = 120</p>
<p style="text-align: justify; font-weight: normal;">Lalu, kita hitung peluang terambil 3 balon kuning sekaligus:</p>
<p style="text-align: justify; font-weight: normal;">P(A) = n(A) / n(S) = 35/120 = 7/24 = 0,29</p>
<p style="text-align: justify; font-weight: normal;">Jadi, jawaban yang tepat untuk contoh soal peluang acak di atas adalah <span style="font-weight: bold;">0,29</span>.</p>
<p style="text-align: justify; font-weight: bold;">Baca Juga: <a href="/blog/teori-peluang-kejadian-majemuk-bagian-1" rel="noopener">Konsep Kejadian Majemuk dalam Teori Peluang Matematika</a></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;"><strong>Pengertian Peluang Komplemen</strong></span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Di materi peluang kejadian ini, juga ada yang namanya peluang komplemen, simbolnya kayak gini nih A<sup>c</sup>. Peluang komplemen sering juga tuh keluar di soal-soal ujian teori peluang. Kalau begitu, apa sih yang dimaksud peluang komplemen? </span><span style="color: #000000;">Jadi, <span style="font-weight: bold;">peluang komplemen (A<sup>c</sup>) adalah peluang semua kejadian yang bukan A</span>.</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;">Rumus Peluang Komplemen</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Peluang kejadian punya hubungan dengan peluang komplemen. Dari hubungan itu lah, kita bisa mendapatkan rumus peluang komplemen. </span><span style="color: #000000;">Hubungan antara peluang kejadian A dengan komplemennya <span style="font-weight: normal;">(A<sup>c</sup>)</span>, antara lain:</span></p>
<p style="text-align: left;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Hubungan%20Peluang%20kejadian%20dan%20Peluang%20komplemen.jpg" alt="Hubungan Peluang kejadian dan Peluang komplemen" width="600" loading="lazy" style="text-align: justify; width: 600px; margin-left: auto; margin-right: auto; display: block;"></span></p>
<p style="text-align: justify; font-size: 16px;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;"><strong>Cara Menghitung Peluang Komplemen</strong></span></h2>
<p><span style="color: #000000;">Diketahui suatu kantong berisi 8 bola merah, 4 bola putih, dan 2 bola hijau. Peluang terambilnya bola bukan merah adalah ….</span></p>
<p style="text-align: justify; font-weight: bold;"><span style="color: #000000;">Pembahasan:</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Misal: P(A)= peluang terambilnya bola merah</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Maka, untuk mencari peluang terambilnya bola merah atau <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-07-55-41-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Yuk kita cari terlebih dahulu P(A) dengan rumus:</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-08-26-96-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;">n(A) adalah banyaknya bola merah dalam kantong, berarti n(A)= 8</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Sedangkan n(S) banyaknya sampel yaitu jumlah semua bola yang ada di kantong,</span></p>
<p style="text-align: justify;"><span style="color: #000000;"> n(S) = 8 + 4+ 2 = 14.</span></p>
<p style="text-align: justify;"><span style="color: #000000;">langsung aja kita substitusi ke rumus: <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-08-58-03-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-09-10-47-AM.png" loading="lazy"></span></p>
<p style="text-align: justify; font-weight: bold;"><span style="color: #000000;">Baca Juga: <a href="/blog/kombinasi-dan-binomial-newton" rel="noopener">Kombinasi dan Binomial Newton dalam Aturan Pencacahan</a></span></p>
<p style="text-align: justify; font-weight: bold;"> </p>
<h2 style="text-align: justify; font-weight: bold; font-size: 20px;"><span style="color: #000000;">Contoh Soal Peluang Komplemen</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Tiga uang koin dilempar secara bersamaan. Peluang tidak muncul gambar satu pun adalah…</span></p>
<p style="text-align: justify; font-weight: bold;"><span style="color: #000000;">Pembahasan:</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Misal: P(A) = peluang munculnya gambar</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Maka, untuk mencari peluang tidak muncul gambar adalah P(A<sup>c</sup>) = 1 – P(A)</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Cari terlebih dahulu P(A) dengan rumus:</span></p>
<p style="text-align: justify;"><span style="color: #000000;">P(A) = n(A) / n(S)</span></p>
<p style="text-align: justify;"><span style="color: #000000;">n(A) adalah banyaknya gambar yang ada pada ruang sampel, berarti n(A) = 7</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Sedangkan n(S) adalah banyaknya sampel, berarti </span><span style="color: #000000;">n(S) = 8 </span></p>
<p style="text-align: justify;"><span style="color: #000000;">Langsung kita substitusi ke rumus: </span></p>
<p style="text-align: justify;"><span style="color: #000000;">P(A) = n(A) / n(S) = 7/8</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Lalu, kita cari peluang komplemennya:</span></p>
<p style="text-align: justify;"><span style="color: #000000;">P(A<sup>c</sup>) = 1 – P(A) = 1 – 7/8 = 8/8 – 7/8 = 1/8 = 0,125</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Jadi, peluang tidak muncul gambar satu pun adalah <span style="font-weight: bold;">0,125</span>.</span></p>
<p style="text-align: justify; font-size: 16px;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;"><strong>Frekuensi Harapan Suatu Kejadian </strong></span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Ketika kamu belajar peluang kejadian, jangan bingung kalo kamu nemuin frekuensi harapan. Frekuensi harapan atau disimbolkan dengan F<sub>h</sub>(A), bisa juga disebut sebagai <span style="font-weight: bold;">ekspektasi suatu kejadian</span>. </span></p>
<p style="text-align: justify;"><span style="color: #000000;">Kalo suatu percobaan dilakukan berulang kali, maka frekuensi harapan muncul suatu kejadiannya akan semakin besar.</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;">Rumus Frekuensi Harapan Suatu Kejadian</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Jadi, <span style="font-weight: bold;">frekuensi harapan pada suatu percobaan adalah hasil kali banyaknya percobaan dengan peluang kejadian secara teoritis</span>. Rumus frekuensi harapan bisa ditulis sebagai berikut:</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rumus%20frekuensi%20harapan%20kejadian.jpg" alt="Rumus frekuensi harapan kejadian" width="600" loading="lazy" style="width: 600px; margin-left: auto; margin-right: auto; display: block;"></span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="color: #000000;"><em>“Biasanya soal frekuensi harapan suatu kejadian kaya gimana sih?”</em></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, langsung masuk ke contoh soal aja yuk!</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-size: 20px;"><span style="color: #000000;"><strong>Cara Menghitung Frekuensi Harapan Suatu Kejadian</strong></span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Sebuah dadu dilempar 24 kali. Jika A adalah kejadian muncul mata dadu prima ganjil, maka tentukanlah frekuensi harapan munculnya kejadian A!</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><em>Pembahasan:</em></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Diketahui dari soal n = 24</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Ingat Rumus Frekuensi Harapan: </strong></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-13-42-50-AM.png" loading="lazy"></strong></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, karena A adalah mata dadu prima ganjil, maka A={3,5}</span></p>
<p style="text-align: justify;"><span style="color: #000000;">atau <em>n(A)</em>= 2. </span></p>
<p style="text-align: justify;"><span style="color: #000000;">Untuk S = {1,2,3,4,5,6} maka <em>n(S)</em>= 6</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Lanjut, tinggal masukan ke dalam rumus frekuensi harapan.</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jun-29-2022-08-14-07-25-AM.png" loading="lazy"></span></p>
<p style="text-align: justify;"><span style="color: #000000;">Jadi, frekuensi harapan kejadian A adalah 8.</span></p>
<p style="text-align: justify;"> </p>
<h2 style="text-align: justify; font-weight: bold; font-size: 20px;"><span style="color: #000000;">Contoh Soal Frekuensi Harapan</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Sudah paham teorinya, sekarang kita latihan soal, yuk! </span></p>
<p style="text-align: justify; font-weight: normal;">Terdapat 7 buah kartu yang ditulisi huruf A, B, C, D, E, F, G. Lalu, dari kartu tersebut diambil sebuah kartu secara acak. Jika pengambilan dilakukan sebanyak 70 kali dengan pengembalian, maka frekuensi harapan terambil kartu yang bertuliskan huruf vokal adalah…</p>
<p style="text-align: justify; font-weight: bold;">Pembahasan:<span style="color: #000000;"></span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">Diketahui: </span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">n(A) = banyaknya huruf vokal yang tersedia yaitu 2 (A dan E)</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">n(S) = banyaknya kartu yaitu 7</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">n = banyaknya pengambilan yaitu 70 kali</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">Maka, frekuensi harapan terambil kartu bertuliskan huruf vokal adalah:</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">f<sub>h</sub>(A) = n x P(A)</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;"> = n x n(A) / n(S)</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;"> = 70 x 2 / 7</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;"> = 20</span></p>
<p style="text-align: justify; font-weight: normal;"><span style="color: #000000;">Jadi, frekuensi harapan terambil kartu bertuliskan huruf vokal adalah <span style="font-weight: bold;">20</span>.</span><span style="color: #000000;"></span></p>
<p style="text-align: justify; font-weight: bold;"><span style="color: #000000;">Baca Juga: <a href="/blog/mengetahui-pengertian-peluang-empirik" rel="noopener">Konsep Dasar Peluang Empiris, Rumus, dan Contoh Soalnya</a></span></p>
<p style="text-align: justify; font-weight: normal;"> </p>
<p style="text-align: justify;"><span style="color: #000000;">Wah, lengkap banget nih pembahasan mengenai peluang ini. Kamu sudah belajar banyak mengenai rumus-rumus peluang kejadian, peluang komplemen, frekuensi harapan, disertai contoh soalnya. Ternyata cukup mudah kan, guys?</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Sebenarnya materi peluang gak berhenti sampai di sini aja ya, karena masih ada lagi pembahasan yang lebih seru. Aku kasih contohnya nih, ada peluang kejadian yang saling lepas, saling bebas, dan masih banyak lagi! Semua materi ini penting loh!</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Makanya jangan sampai kelewatan untuk terus belajar dan bahas-bahas soal di <a href="https://ruangguru.onelink.me/blPk/eaff0eb9" rel="noopener" target="_blank"><strong>ruangbelajar</strong></a>. Materinya lengkap, pembahasan soal yang terupdate terus-menerus ditambah lagi pembahasan soal nya gampang dipahami, langganan sekarang aja yuk.</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Sampai jumpa di artikel berikutnya ya, dadah!</span></p>
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<p style="text-align: justify;"><span style="color: #000000;"><strong>Referensi:</strong></span></p>
<p style="text-align: left;"><span style="color: #000000;">Nugraha, S dan Sulaiman. (2012) Buku Jagoan Matematika SMA/MA Kelas 10,11,12. Depok: Penerbit Pustaka Makmur.</span></p>
<p style="text-align: left;"><span style="color: #000000;">Sutrisno, J. dan Foster, B. (2019) Fokus Belajar Inti Sari Matematika untuk SMP/MTs. Jakarta: Penerbit Duta.</span></p>
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<p style="text-align: left; font-weight: bold;"><em>Artikel pertama kali ditulis oleh Tedy Rizkha Heryansyah dan diperbarui pada 29 Juni 2022 oleh Efira Yesika.</em></p>
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<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>