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A total of 2n cards, of which 2 are aces, are to be
Chapter 3, Problem 28STE(choose chapter or problem)
Problem 28STE
A total of 2n cards, of which 2 are aces, are to be randomly divided among two players, with each player receiving n cards. Each player is then to declare, in sequence, whether he or she has received any aces. What is the conditional probability that the second player has no aces, given that the first player declares in the affirmative, when (a) n = 2? (b) n = 10? (c) n = 100? To what does the probability converge as n goes to infinity? Why?
Questions & Answers
QUESTION:
Problem 28STE
A total of 2n cards, of which 2 are aces, are to be randomly divided among two players, with each player receiving n cards. Each player is then to declare, in sequence, whether he or she has received any aces. What is the conditional probability that the second player has no aces, given that the first player declares in the affirmative, when (a) n = 2? (b) n = 10? (c) n = 100? To what does the probability converge as n goes to infinity? Why?
ANSWER:
Step 1 of 2
Here we need to find the conditional probability that the second player has no aces, given that the first player declares in the affirmative, when, (a). n = 2, (b). n = 10, (c). n = 100.
Let us denote Second player gets Ace.
First player gets Ace.
Second player does not get Ace.