SOLUTION: of two men,it is said that one sometimes tells the truth,while the other only tells the truth two times out of three. If one is chosen at random and asked a question,the probabilit

Question 698100: of two men,it is said that one sometimes tells the truth,while the other only tells the truth two times out of three. If one is chosen at random and asked a question,the probability of a truthfully answer is 17/24.how often does the first man tell the truth.
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
The probability you get a truthful answer is equal to the sum of the probability of selecting each person and then getting a truthful answer from him. In this problem, a man is chosen at random, so there is a 1/2 chance you ask the person who is truthful 2/3 of the time, and a 1/2 chance you ask the person who has an unknown truthfulness rate. The sum of the products of picking each person and their respective probabilities of telling the truth is 17/24, so you can set up the equation:
(1/2)*x + (1/2)*(2/3) = 17/24, where x is the probability the unknown man tells the truth.

(1/2)*x + 1/3 = 17/24
(1/2)*x + 8/24 = 17/24
(1/2)*x = 9/24
x = 18/24 = 3/4

So the other person tells the truth 3/4 times.
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