Conditional Probability Practice

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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 reads as 'the probability of A given B'.

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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 ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

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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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What is the formula for Total Probability?

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The Total Probability theorem 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 the Complement Rule in probability?

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The Complement Rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring: P(A') = 1 - P(A).

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What is the difference between independent and dependent events?

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Independent events are those whose occurrence does not affect the probability of another event occurring. Dependent events are those where the occurrence of one event affects the probability of another event.

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How do you determine if two events are independent?

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Two events A and B are independent if P(A ∩ B) = P(A) * P(B). If this equality holds, the events are independent.

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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 a joint probability?

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Joint probability is the probability of two events occurring together. It is denoted as P(A ∩ B).

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What is a marginal probability?

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Marginal probability is the probability of an event occurring without consideration of any other events. It is denoted as P(A) or P(B).