A speaks truth in 80% cases and B speaks truth in 90% cases. In what percentage of cases are they likely to agree with each other in stating the same fact?

Given: A speaks truth in 80% cases and B speaks truth in 90% cases.

To Find: Probability of them agreeing with each other.

In case of they agree with each other, that means either they both speak truth or they both speak false.

Let, P(A) = case of A speaks truth =

P(B) = case of B speaks truth =

Similarly, P(A’) = = case of A speaks false and P(B’) = = case of B speaks false.

So, when both they agree with each other,

P(A) x P(B) + P(A’) x P(B’)

=

=

So, in 74% cases they agree with each other.