Question

A and B are two independent witnesses (i.e.,there is no collusion between them) in a case. The probability that A will speak the truth is x, and the probability that B will speak the truth is y. A and B agree in a certain statement. Then the probability that this statement is true is:

Answer 1

The probability that the statement is true when both A and B agree is P(A) * P(B).

Step-by-step explanation:

When two independent witnesses A and B agree on a statement, we want to find the probability that the statement is true.

We can use the Product Rule to determine this probability. For independent events A and B, the probability of both events occurring is given by P(AB) = P(A) * P(B).

So, the probability that the statement is true when both A and B agree is P(A) * P(B), where P(A) represents the probability that A speaks the truth and P(B) represents the probability that B speaks the truth.