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)$
$=\frac{4}{5} \times \frac{1}{4}+\frac{1}{5} \times \frac{3}{4}$
$=\frac{1}{5}+\frac{3}{20}=\frac{7}{20}$