Question

A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement, is
(a) $\frac{7}{20}$

(b) $\frac{13}{20}$

(c) $\frac{3}{5}$

(d) $\frac{2}{5}$

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\frac{7}{20} \\ P\left(\text{A speaks truth}\right)=0.75 \\ P\left(\text{A lies}\right)=1-0.75=0.25 \\ \text{P}\left(\text{B speaks truth}\right)=0.8 \\ P\left(\text{B lies}\right)=1-0.8=0.2 \\ P\left(\text{contradicting each other in a statement}\right)=\text{P(A speaks truth and B lies)+P}\left(\text{B speaks truth and A lies}\right) \\ =0.75\times 0.2+0.8\times 0.25 \\ =0.15+0.2 \\ =0.35 \\ =\frac{35}{100}=\frac{7}{20} \end{gathered}$$