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Sports and Leisure

Suppose two cards are drawn without replacement from a regular deck of 52 playing cards. Consider the events A1 5 an ace is selected on the first draw; A2 5 an ace is selected on the second draw.

a. Find P(A2 | A1) and P(A2). Are the events A1 and A2 independent? Justify your answer.

b. Suppose the two cards are drawn without replacement from six regular 52-card decks shuffled together. Find P(A2 | A1) and P(A2) for this experiment. Are the events A1 and A2 independent? Justify your answer.

c. In part (b), the events are almost independent. For six decks, find P(A1 ∩ A2) exactly, and then find the same probability assuming the two events are independent (with the probability of an ace on any draw being 24/312).

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Category:- Statistics and Probability
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