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There are 4 married couples attending a party. Two identical door prizes are randomly awarded to two different people.
Answer the following questions. (Give your answers correct to three decimal places.)
(a) What is the probability one prize goes to a man and one to a woman?
(b) What is the probability a married couple wins both of the prizes?
(c) John and Mary are one of the married couples at the party. If Mary wins a prize, what is the conditional probability that John will win the other prize?
(d) If Mary does not win a prize, then what is the conditional probability that John will win one of the two prizes?
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