PROBLEM 4. Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets that he cannot and, in fact, just guesses. To settle this, a bet is made: Charles is to be given ten small glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the probability that Ruth wins if Charles is guessing.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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PROBLEM 4. Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets
that he cannot and, in fact, just guesses. To settle this, a bet is made: Charles is to be given ten small
glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets
seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the
probability that Ruth wins if Charles is guessing.
Transcribed Image Text:PROBLEM 4. Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets that he cannot and, in fact, just guesses. To settle this, a bet is made: Charles is to be given ten small glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the probability that Ruth wins if Charles is guessing.
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