Question

A man A speaks truth in $80\%$ of the cases and another man B in $90\%$ of the cases. While stating the same fact, what is the probability that they contradict?

• A. $\frac{37}{50}$
• B. $\frac{13}{50}$
• C. $\frac{16}{50}$
• D. None of these

Answer 1

The correct option is B $\frac{13}{50}$

Probability (contradiction)
=P(A speaks truth) $\times$ P(B does not speak truth) + P (A does not speak truth) $\times$ P(B speaks truth)
$=\frac{80}{100}\times \frac{10}{100}+\frac{20}{100}\times \frac{90}{100}$
$=\frac{8}{100}+\frac{18}{100}=\frac{26}{100}=\frac{13}{50}$