Question

A speaks truth in $75\%$ cases and B in $80\%$ of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident?

• A. $5\%$
• B. $15\%$
• C. $35\%$
• D. $45\%$

Answer 1

The correct option is C $35\%$

A Speak truth $75\%$ i.e. P(A) = $\frac{3}{4},P\left(\overline{A}\right)=\frac{1}{4}$
Similarly, B Speak truth $80\%$ i.e. P(B) = $\frac{4}{5},P\left(\overline{B}\right)=\frac{1}{5}$
While contradicting the narration
Probaility = $P\left(A\right)P\left(\overline{B}\right)+P\left(\overline{A}\right)PB$
= $\frac{3}{4}\times \frac{1}{5}+\frac{1}{4}\times \frac{4}{5}$
= $\frac{7}{20}=\frac{7}{20}\times 100\%=35\%$