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 means the probability of event A given event B.

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What is the formula for Conditional Probability?

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The formula for Conditional Probability is 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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How do you interpret P(B|A)?

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

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What is the relationship between independent events and Conditional Probability?

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For independent events, the occurrence of one event does not affect the probability of the other. Thus, P(A|B) = P(A) and P(B|A) = P(B).

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If P(A) = 0.5 and P(B) = 0.4, what is P(A|B) if A and B are independent?

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If A and B are independent, then P(A|B) = P(A) = 0.5.

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What is the complement of an event?

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The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is P(A') = 1 - P(A).

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How do you calculate the probability of the union of two events?

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The probability of the union of two events A and B is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

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What is Bayes' Theorem?

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Bayes' Theorem relates the conditional and marginal probabilities of random events. It is expressed as P(A|B) = [P(B|A) * P(A)] / P(B).

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What is an example of Conditional Probability in real life?

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An example of Conditional Probability is determining the probability of a person being a smoker given that they have lung cancer.