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 means 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 and B) / P(B), where P(A and B) is the probability of both events 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 formula states that P(A) = P(A|B)P(B) + P(A|not B)P(not B).

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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 Complement Rule in probability?

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The Complement Rule states that the probability of an event not occurring is 1 minus the probability of the event occurring: P(not 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 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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How do you find P(A|B) when given a contingency table?

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To find P(A|B) from a contingency table, divide the number of occurrences of A and B by the total occurrences of B.

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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 an example of Conditional Probability in real life?

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An example of Conditional Probability is determining the probability of a person being a smoker given that they have lung cancer.