The probability that A speaks truth is $\dfrac{4}{5}$ while this probability for B is $\dfrac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is:

The correct answer is $\dfrac{7}{20}$

The probability that A speaks truth

P(A) = $\dfrac{4}{5}$

Hence, the probability that A speaks a lie

P(A') = $1 - \dfrac{4}{5} = \dfrac{1}{5}$


The probability that B speaks truth

P(B) = $\dfrac{3}{4}$

Hence, the probability that B speaks a lie

P(B') = $1 - \dfrac{3}{4} = \dfrac{1}{4}$



The probability of they contradict each other

$P(A)P(B') + P(A')P(B)$
= $\dfrac{4}{5} \times \dfrac{1}{4}$ + $\dfrac{1}{5} \times \dfrac{3}{4}$
= $\dfrac{1}{5}$ + $\dfrac{3}{20}$ = $\dfrac{7}{20}$