Conditional Probability

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What is Conditional Probability?

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

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How is Conditional Probability calculated?

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P(A|B) = P(A and B) / P(B), where P(A and B) is the joint probability of both events occurring.

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What does P(A|B) represent?

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It represents the probability of event A occurring given that event B has occurred.

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If P(A) = 0.5 and P(B) = 0.4, and P(A and B) = 0.2, what is P(A|B)?

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P(A|B) = P(A and B) / P(B) = 0.2 / 0.4 = 0.5.

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What is the Law of Total Probability?

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It states that the total probability of an event can be found by considering all possible ways that event can occur, often using conditional probabilities.

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What is Bayes' Theorem?

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A formula that describes how to update the probability of a hypothesis based on new evidence: P(A|B) = [P(B|A) * P(A)] / P(B).

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What is the difference between independent and dependent events?

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Independent events do not affect each other's probabilities, while dependent events do.

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If two events A and B are independent, what is P(A and B)?

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P(A and B) = P(A) * P(B).

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What is the complement of an event?

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

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What is a joint probability?

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The probability of two events occurring together, denoted as P(A and B).