• # question_answer The probability that A speaks the  truth is $3\text{ }/5$ and probability that B speaks the truth is$3\text{ }/4$ Find the probability that they contradict each other when; asked to speak a fact. A)  $3/20$                 B)  $4/5$ C)  $9/20$                D)  $7/20$

Given, probability that A speaks truth $P(A)=\frac{3}{5}$ $\therefore$ Probability that A not speaks truth, $P(\bar{A})$ $=1-\frac{3}{5}=\frac{2}{5}$ Probability that B speaks the truth, $P(B)=\frac{3}{4}$ $\therefore$ Probability that B not speaks truth, $P(\bar{B})=1-\frac{3}{4}$   $=\frac{1}{4}$ Required probability $=P(A)P(\bar{B})+P(\bar{A})P(B)$ $=\frac{3}{5}\times \frac{1}{4}+\frac{2}{5}\times \frac{3}{4}=\frac{3}{20}+\frac{6}{20}=\frac{9}{20}$