Question

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

• A. $\frac{3}{23}$
• B. $\frac{1}{20}$
• C. $\frac{1}{5}$
• D. $\frac{14}{40}$

Answer 1

The correct option is D

$\frac{14}{40}$

In short the event described here is P(A)'P(B) +P(A)P(B)'

where P(A) and P(B) are the probabilities of A and B speaking the truth respectively.

P(E)= P(A)'P(B) +P(A)P(B)' = $\frac{1}{5}\times \frac{3}{4}+\frac{4}{5}\times \frac{1}{4}$

P(E)=$\frac{3}{20}+\frac{4}{20}=\frac{7}{20}=\frac{14}{40}$