Three men were walking down a street talking when they met a fourth man. If the fourth man knew that two of the men always lied and the third always told the truth and he asked the three a question, what is the probability that he got a truthful answer when one man answered?
1/3
He asks three person a question, and only one of them tells the truth. The probability of getting the truthful man to answer is 1/3
To calculate the probability that the fourth man received a truthful answer when one man answered, we first need to analyze the situation.
Let's assign names to the four men for simplicity: A, B, C, and D. According to the problem, two of them always lie (A and B), one always tells the truth (C), and the identity of the fourth man (D) is unknown.
When the fourth man asked the question, there are three possible situations:
Case 1: The truthful man (C) answers.
Case 2: One of the lying men (A or B) answers.
Case 3: The unknown man (D) answers.
In Case 1, as the truthful man always tells the truth, the probability of receiving a truthful answer is 100% (or 1).
In Case 2, one of the lying men (A or B) could answer. Given that both of them always lie, the probability of receiving a truthful answer in this case is 0% (or 0).
In Case 3, since D's identity is unknown, we don't have enough information to calculate the probability of receiving a truthful answer. The probability could vary depending on whether D happens to be a liar or a truth-teller.
Given that the three possible situations (cases) are equally likely, we can calculate the overall probability by taking the average probability of the truthful answer occurring in each case.
The probability in Case 1 is 1, in Case 2 is 0, and in Case 3 is unknown. Since we don't know the probability in Case 3, we cannot definitively calculate the exact probability that the fourth man received a truthful answer when one man answered.