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2026-01-01
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2026-02-28
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<p>Formulas of probability and statistics help us solve complex mathematical problems easily, and they aid in making well-informed decisions and conclusions. Here are some of the common<a>formulas</a>of probability and statistics: </p>
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<p>Formulas of probability and statistics help us solve complex mathematical problems easily, and they aid in making well-informed decisions and conclusions. Here are some of the common<a>formulas</a>of probability and statistics: </p>
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<p><strong>Probability Formulas</strong></p>
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<p><strong>Probability Formulas</strong></p>
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<p>Probability is a measure used to calculate the likelihood of an event occurring. The formula for calculating probability is: </p>
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<p>Probability is a measure used to calculate the likelihood of an event occurring. The formula for calculating probability is: </p>
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<p>P(A) = Number of favorable outcomes ÷ Total number of possible outcomes</p>
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<p>P(A) = Number of favorable outcomes ÷ Total number of possible outcomes</p>
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<p>Here, P(A) is the probability of an event A happening.</p>
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<p>Here, P(A) is the probability of an event A happening.</p>
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<p>Favorable outcomes are the cases where event A happens. </p>
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<p>Favorable outcomes are the cases where event A happens. </p>
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<p>The total number of possible outcomes is the total number of results.</p>
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<p>The total number of possible outcomes is the total number of results.</p>
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<p>The probability of an event that is certain is 1. The probability of an event that is impossible to happen is 0. So, the values of probability always lie between 1 and 0. Probability can be written in a<a>percentage</a>format by multiplying the given value by 100. </p>
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<p>The probability of an event that is certain is 1. The probability of an event that is impossible to happen is 0. So, the values of probability always lie between 1 and 0. Probability can be written in a<a>percentage</a>format by multiplying the given value by 100. </p>
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<p>For instance, the probability of getting heads when tossing a fair coin is:</p>
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<p>For instance, the probability of getting heads when tossing a fair coin is:</p>
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<p>P(Heads) = \(\frac{1}{2}\)</p>
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<p>P(Heads) = \(\frac{1}{2}\)</p>
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<p>A fair coin has two sides, and only one of them is a head:</p>
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<p>A fair coin has two sides, and only one of them is a head:</p>
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<p>P(Heads) \(=\frac{1}{2} = 0.5 = 50%\)</p>
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<p>P(Heads) \(=\frac{1}{2} = 0.5 = 50%\)</p>
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<p><strong>Addition Rule Formula</strong> </p>
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<p><strong>Addition Rule Formula</strong> </p>
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<p>To calculate the probability that at least one of the two<a>mutually exclusive events</a>will occur, we can use the<a>addition</a>rule of probability. In the formula for mutually exclusive events with no overlap, the likelihood of either event A or B happening is calculated by adding their probabilities separately. If A and B are mutually exclusive events, then: </p>
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<p>To calculate the probability that at least one of the two<a>mutually exclusive events</a>will occur, we can use the<a>addition</a>rule of probability. In the formula for mutually exclusive events with no overlap, the likelihood of either event A or B happening is calculated by adding their probabilities separately. If A and B are mutually exclusive events, then: </p>
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<p>(A or B) \(= P(A ∪ B) = P(A) + P(B)\) </p>
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<p>(A or B) \(= P(A ∪ B) = P(A) + P(B)\) </p>
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<p>For non-mutually exclusive events with overlapping, the formula is: </p>
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<p>For non-mutually exclusive events with overlapping, the formula is: </p>
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<p>P(A or B) \(= P(A ∪ B) = P(A) + P(B) - P(A ∩ B) \)</p>
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<p>P(A or B) \(= P(A ∪ B) = P(A) + P(B) - P(A ∩ B) \)</p>
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<p><strong>Multiplication Rule Formula </strong></p>
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<p><strong>Multiplication Rule Formula </strong></p>
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<p>We can use this formula to calculate the probability of two<a>independent events</a>happening together. The probability of both events happening, if A and B are dependent on one another, is equal to the<a>product</a>of the probability of A and the<a>conditional probability</a>of B, given that A has happened. </p>
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<p>We can use this formula to calculate the probability of two<a>independent events</a>happening together. The probability of both events happening, if A and B are dependent on one another, is equal to the<a>product</a>of the probability of A and the<a>conditional probability</a>of B, given that A has happened. </p>
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<p>\(P(A ∩ B) = P(A) × P(B∣A)\)</p>
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<p>\(P(A ∩ B) = P(A) × P(B∣A)\)</p>
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<p>Here, P(B∣A) is the probability of B happening after A has already happened. </p>
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<p>Here, P(B∣A) is the probability of B happening after A has already happened. </p>
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<p><strong>Bayes’ Rule</strong></p>
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<p><strong>Bayes’ Rule</strong></p>
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<p>This method is used to update probabilities when new information is available. It determines the likelihood that event A will occur given the occurrence of event B. </p>
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<p>This method is used to update probabilities when new information is available. It determines the likelihood that event A will occur given the occurrence of event B. </p>
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<p>\(P(A∣B) = \frac{P(B∣A) × P(A)}{P(B)}\)</p>
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<p>\(P(A∣B) = \frac{P(B∣A) × P(A)}{P(B)}\)</p>
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<p>Here, P(A|B) is the probability of A happening given that B has occurred.</p>
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<p>Here, P(A|B) is the probability of A happening given that B has occurred.</p>
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<p>P(B|A) is the probability of B happening given that A has occurred. </p>
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<p>P(B|A) is the probability of B happening given that A has occurred. </p>
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<p>P(A) and P(B) are the individual probabilities of A and B.</p>
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<p>P(A) and P(B) are the individual probabilities of A and B.</p>
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<p>Other important rules related to probability are given below: </p>
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<p>Other important rules related to probability are given below: </p>
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<ul><li>The probability is between 0 and 1: If an event cannot happen, then its probability is 0. If an event is sure to happen, its probability is 1. </li>
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<ul><li>The probability is between 0 and 1: If an event cannot happen, then its probability is 0. If an event is sure to happen, its probability is 1. </li>
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</ul><ul><li>The sum of all probabilities is 1: The<a>sum</a>of all possible outcomes equals 1 or 100%. </li>
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</ul><ul><li>The sum of all probabilities is 1: The<a>sum</a>of all possible outcomes equals 1 or 100%. </li>
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</ul><ul><li>Complement rule: An event's likelihood of occurring (P(A)) plus its likelihood of not occurring (P(not A)) = 1. One common way to write P(not A) is 1 - P(A). </li>
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</ul><ul><li>Complement rule: An event's likelihood of occurring (P(A)) plus its likelihood of not occurring (P(not A)) = 1. One common way to write P(not A) is 1 - P(A). </li>
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</ul>
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</ul>