Conditional Probability

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What is Conditional Probability?

Back

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 Bayes' Theorem?

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P(A|B) = [P(B|A) * P(A)] / P(B) where P(B) is the total probability of B.

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

Front

What is the complement of an event?

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The probability that the event does not occur, calculated as 1 - P(A).

Front

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) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

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What is an example of Conditional Probability in real life?

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

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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.

Front

How do you interpret P(A|B) = 0.3?

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There is a 30% chance that event A occurs given that event B has occurred.