Question

A man speaks truth in 80% of the cases and another 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 $\frac{13}{50}$

Let the two men be A and B

A : A speaks truth
B : B speaks truth

$P\left(A\right)=\frac{80}{100}\Rightarrow P\left(\overline{A}\right)=1-P\left(A\right)=1-\frac{80}{100}$

$P\left(B\right)=\frac{90}{100}\Rightarrow P\left(\overline{B}\right)=1-P\left(B\right)=1-\frac{90}{100}$


$\therefore Requiredprobability$

$=P\left(A\right)P\left(\overline{B}\right)+P\left(B\right)P\left(\overline{A}\right)$

$=\frac{80}{100}\times \frac{10}{100}+\frac{90}{100}\times \frac{20}{100}$

$=\frac{8+18}{100}=\frac{26}{100}=\frac{13}{50}$