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Original
2026-01-01
Modified
2026-02-28
1
<p>{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}</p>
1
<p>{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}</p>
2
<p>The above are all the possible outcomes that have equal probability.</p>
2
<p>The above are all the possible outcomes that have equal probability.</p>
3
<p>For example, let's consider throwing two dice at the same time. Probability of rolling a 1 on the first die and a 5 on the second die (or vice versa) is given as, </p>
3
<p>For example, let's consider throwing two dice at the same time. Probability of rolling a 1 on the first die and a 5 on the second die (or vice versa) is given as, </p>
4
<p>First, let us calculate the probability of rolling a 1 on the first die and a 5 on the second die</p>
4
<p>First, let us calculate the probability of rolling a 1 on the first die and a 5 on the second die</p>
5
<p>\(P(1, 5) = \frac{1}{6} \times \frac {1}{6} = \frac{1}{36}\)</p>
5
<p>\(P(1, 5) = \frac{1}{6} \times \frac {1}{6} = \frac{1}{36}\)</p>
6
<p>The probability of rolling a 5 on the first die and a 1 on the second die is, </p>
6
<p>The probability of rolling a 5 on the first die and a 1 on the second die is, </p>
7
<p>\(P(5, 1) = \frac{1}{6} \times \frac {1}{6} = \frac {1}{36}\)</p>
7
<p>\(P(5, 1) = \frac{1}{6} \times \frac {1}{6} = \frac {1}{36}\)</p>
8
<p>Since these events are mutually exclusive, let us add their probabilities. </p>
8
<p>Since these events are mutually exclusive, let us add their probabilities. </p>
9
<p>\(\)\(P(1, 5) + P(5, 1) = \frac{1}{36} + \frac{1}{36} = \frac{2}{36}\)</p>
9
<p>\(\)\(P(1, 5) + P(5, 1) = \frac{1}{36} + \frac{1}{36} = \frac{2}{36}\)</p>
10
<p>therefore, the probability is, </p>
10
<p>therefore, the probability is, </p>
11
<p>\(P = \frac{1}{18}\)</p>
11
<p>\(P = \frac{1}{18}\)</p>