Question

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

• A. $\frac{3}{20}$
• B. $\frac{1}{5}$
• C. $\frac{7}{20}$
• D. $\frac{4}{5}$

Answer 1

Answer: (C)

Given probabilities of speaking truth are
$P(A)=\frac{4}{5}$
$\text{ and }P(B)=\frac{3}{4}$
and their corresponding probabilities of not speaking truth are
$P(\bar{A})=\frac{1}{5}$
$\text{ and }P(B)=\frac{1}{4}$
$\therefore \text{ Required probability }=P(A)\times P(\bar{B})+P(\bar{A})\times P(B)$
$=\frac{4}{5}\times \frac{1}{4}+\frac{1}{5}\times \frac{3}{4}$
$=\frac{1}{5}+\frac{3}{20}=\frac{7}{20}$