A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?

Do you think that statement of B is true?

P(A speaking truth)

P(A speaking lie)

P(B speaking truth)

P(B speaking lie)

Cases are when they contradict each other in stating same fact are when A speaks truth and B speaks lie or when A speaks lie and B speaks truth.

⇒ P (contradicting each other) = 0.75×0.1 + 0.25×0.9

= 0.075 + 0.225=0.3

Percentage of cases where they contradict each other in stating the same fact = 0.3× 100 = 30%

In such situation, the statement of B can either be true or false.