Conditional Probability

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What is Conditional Probability?

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

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How is Conditional Probability calculated?

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Conditional Probability is calculated using the formula: P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring and P(B) is the probability of event B.

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What does P(Female | Part-time) represent?

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P(Female | Part-time) represents the probability that a student is female given that they are a part-time student.

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

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

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What is the significance of the denominator in the conditional probability formula?

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The denominator, P(B), represents the total probability of the condition being true. It normalizes the probability of A occurring under the condition of B.

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What is the relationship between independent events and conditional probability?

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For independent events, P(A|B) = P(A). This means the occurrence of event B does not affect the probability of event A.

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What is the probability that a student plays a sport given they do not play an instrument?

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This is an example of conditional probability, which can be calculated using the relevant data.

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What does P(Pizza|Senior) indicate?

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P(Pizza|Senior) indicates the probability that a student eats pizza given that they are a senior.

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How do you interpret P(Sandals|Pants)?

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P(Sandals|Pants) indicates the probability that a student wears sandals given that they are wearing pants.

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What is the formula for finding P(A and B)?

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