Conditional Probability

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What is Conditional Probability?

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Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads as 'the probability of A given B'.

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How is Conditional Probability calculated?

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Conditional Probability is calculated using the formula: P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

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What does P(A|B) represent?

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P(A|B) represents the probability of event A occurring given that event B has occurred.

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What is the formula for the probability of the complement of an event?

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The probability of the complement of an event A is given by P(A') = 1 - P(A), where A' is the complement of A.

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What is the relationship between independent events and conditional probability?

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For independent events A and B, P(A|B) = P(A). This means the occurrence of B does not affect the probability of A.

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What is the probability that a randomly selected student does not do community service if they do not play sports?

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What is the probability that a randomly selected student is not in a club?

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What is the probability that a randomly selected student plays sports given that they do not do community service?

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What is the probability that a randomly selected student plays sports and does not participate in community service?

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What is the probability that a student plays sports given that they do community service?

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