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 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.

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

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P(A and B) = P(A|B) * P(B). This formula helps in finding the joint probability of two events.

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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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If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

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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. For dependent events, the occurrence of one event changes the probability of the other.

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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 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).

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If P(A) = 0.7, what is P(A')?

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P(A') = 1 - P(A) = 1 - 0.7 = 0.3.