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 A given B.

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What does P(A | B) represent?

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P(A | B) represents the probability of event A occurring given that event B has occurred.

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How do you calculate Conditional Probability?

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Conditional Probability can be 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.

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What is the difference between independent and dependent events?

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Independent events are those whose outcomes do not affect each other, while dependent events are those where the outcome of one event affects the outcome of another.

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If P(A) = 0.5 and P(B) = 0.3, what is P(A and B) if A and B are independent?

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If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.3 = 0.15.

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What is the Law of Total Probability?

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The Law of Total Probability states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire 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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Bayes' Theorem relates the conditional and marginal probabilities of random events. It is expressed as: P(A | B) = [P(B | A) * P(A)] / P(B).

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What is the probability of selecting a male given that a student likes sports?

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This is an example of conditional probability, denoted as P(male | sports). It requires data on the number of males who like sports.

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What does it mean if P(A | B) = P(A)?

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If P(A | B) = P(A), it indicates that events A and B are independent; the occurrence of B does not affect the probability of A.

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What is the complement of an event?

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The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is given by P(A') = 1 - P(A).