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.

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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|B) is the probability of A given B.

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What does P(A|B) represent?

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The probability of event A occurring given that event B has occurred.

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What is the formula for finding the probability of two independent events?

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P(A and B) = P(A) * P(B) for independent events.

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

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P(A and B) = 0.4 * 0.5 = 0.2.

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What is the complement of an event?

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The complement of an event A is the event that A does not occur, denoted as A'.

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If P(A) = 0.3, what is P(A')?

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P(A') = 1 - P(A) = 1 - 0.3 = 0.7.

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What is the Law of Total Probability?

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If B1, B2, ..., Bn are disjoint events that cover the sample space, then P(A) = Σ P(A|Bi) * P(Bi).

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What is Bayes' Theorem?

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P(A|B) = [P(B|A) * P(A)] / P(B), used to find conditional probabilities.

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What is an example of Conditional Probability in real life?

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The probability of a person being a smoker given that they have lung cancer.