Question

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

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

Answer 1

Answer: (C)

$\frac{7}{20}$

Answer 2

A and B will contradict each other if one speaks truth and other false. So, the required Probability $= \frac{4}{5} \left(1- \frac{3}{4}\right) + \left(1- \frac{4}{5}\right) \frac{3}{4}$ $= \frac{4}{5} \times\frac{1}{4}+ \frac{ 1}{5} \times\frac{3}{4} = \frac{7}{20}$