Edited by Richard Walker, Friday 6 November 2026 at 01:20
This is 7.1 in Bogomolny's book.
A and B both tell the truth with probability and lie with .
A makes a statement which B confirns is true.
What is the probability that A's statement is in fact true?
Scroll down for a solution.
Solution
A and B might both be telling the truth or they might both be lying.
But from the given information it can't be the case that A is telling the truth and B is lying, because B's confirmation would the truth and not a lie.
Similarly it can't be be the case that A is lying and B is telling the truth, because B's confirmation would be a lie and not the truth.
So we cam draw this diagram, in which the shaded areas are excluded because they represent situations that are ruled out by the arguments above.
The remaining area is in total, of which represents A telling the truth. Hence the probability that A is telling the truth is
Another Probability Riddle from the Book
This is 7.1 in Bogomolny's book.
Scroll down for a solution.
Solution
A and B might both be telling the truth or they might both be lying.
But from the given information it can't be the case that A is telling the truth and B is lying, because B's confirmation would the truth and not a lie.
Similarly it can't be be the case that A is lying and B is telling the truth, because B's confirmation would be a lie and not the truth.
So we cam draw this diagram, in which the shaded areas are excluded because they represent situations that are ruled out by the arguments above.
The remaining area is in total, of which represents A telling the truth. Hence the probability that A is telling the truth is