Conditional Probability

Front

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 mathematically represented?

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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 is the formula for Total Probability?

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P(A) = P(A|B)P(B) + P(A|¬B)P(¬B), where ¬B is the complement of B.

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What does P(A and B) represent?

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The probability that both events A and B occur.

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

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

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What is the probability of drawing a red marble from a bag with 3 red, 2 blue, and 4 yellow marbles?

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P(Red) = 3/9 = 1/3.

Front

What is the probability that a student plays on a sports team given they play an instrument?

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P(Sports Team | Instrument) = 0.7273.

Front

What is Bayes' Theorem?

Back

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 probability that a person speaks French given they are a girl?

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P(French | Girl) = 0.4.