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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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 Conditional Probability?

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P(A|B) = P(A and B) / P(B), provided P(B) > 0.

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What are Independent Events?

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Two events A and B are independent if the occurrence of one does not affect the occurrence of the other.

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How do you determine if two events are independent?

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Check if P(A|B) = P(A) or P(B|A) = P(B). If true, they are independent.

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What is the Complement Rule in probability?

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The probability of an event not occurring is 1 minus the probability of the event occurring: P(A') = 1 - P(A).

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What is the Total Probability Theorem?

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If B1, B2, ..., Bn are mutually exclusive events that cover the sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

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What is Bayes' Theorem?

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A way to find a conditional probability when you know the reverse conditional probability: P(A|B) = [P(B|A) * P(A)] / P(B).

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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.

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What is an example of Conditional Probability?

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The probability of a student passing a test given that they studied for it.