Question

Ajith speaks truth in 3 out of 4 cases and Vignesh lies in 1 out of 5 cases. What is the percentage of cases in which both Ajith and Vignesh contradict each other in stating a fact?

• A. 45%
• B. 35%
• C. 65%
• D. None of these

Answer 1

The correct option is B

35%

Ajith and Vignesh will contradict each other when one speaks truth and the other lies.

Probability that Ajith speaks the truth and Vignesh lies = $\frac{3}{4}$*$\frac{1}{5}$=$\frac{3}{20}$

Probability that Vignesh speaks the truth and Ajith lies = $\frac{4}{5}$*$\frac{1}{4}$=$\frac{1}{5}$

The two probabilities are mutually exclusive.

Hence, probability that Ajith and Vignesh contradict each other = $\frac{3}{20}$+$\frac{1}{5}$=$\frac{7}{20}$ = 35%