Four men were walking down a street talking when they met a fifth man. If the fifth man knew that only three of the men
always lied and the fourth always tells the truth and he asked the four a question, what is the probability that he
was told a lie when one man answered?
The probability that he was told a lie is
(Simplify your answer.)

In this scenario, there are four men: three liars and one truth-teller. When the fifth man asks a question, he’s likely to receive responses from the liars who will always lie and the truth-teller who will tell the truth. Since there are three liars and only one truth-teller, the probability that any one answer he receives is a lie is calculated as follows:

Out of the four men, if he hears from one, the odds of that one being a liar is 3 out of 4. Thus, the probability that he was told a lie when one man answered is 3/4, or 0.75 when expressed as a decimal.

The solution simplifies to 3/4.