Question

After law school, you visit an island where everybody is a truth-teller or a liar, and get caught up in a criminal trial. The prosecutor, who is either a truth-teller or liar herself, says: X is guilty. X and Y are not both guilty. Can we determine who is guilty and who is innocent?

Answer 1

No, we cannot determine who is guilty and who is innocent.

Explanation:

The prosecutor is either a truth teller or a liar.

The probability of her telling the truth is 0.5, which is the same probability of her telling lies.

Now, she said: X is guilty.

We cannot determine who is guilty and who is innocent, because X and Y both have equal chances of being guilty or innocent, which is due to the equal chances of her telling the truth, and telling a lie.