JIPMAT 2024 (QA) - A speaks the truth in 75 \% cases and B in 80 \% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident? | PYQs + Solutions

JIPMAT 2024

Modern Math

Probability

Medium

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

5 \%

15 \%

35 \%

45 \%

Correct Option: 3

\begin{aligned} & A(\text {truth})=75 \% \rightarrow \frac{3}{4} ;\quad A(\text {not truth})=25 \% \rightarrow\frac{1}{4} \\ & B(\text {truth})=80 \% \rightarrow \frac{4}{5} ;\quad B(\text {not truth})=20 \%\rightarrow \frac{1}{5} \end{aligned}

They will contradict each other when one is telling the truth & the other one is not.

So, two cases are possible:

1) A telling truth, B lying.

\newline

2) A lying, B telling truth.

\begin{aligned} & \therefore A(\text {truth}) \times B(\text {lie})+B(\text {truth}) \times A(\text {lie}) \\ \\ & \Rightarrow \frac{3}{4} \times \frac{1}{5}+\frac{4}{5} \times \frac{1}{4} \\ \\ & =\frac{3}{20}+\frac{1}{5}=\frac{3}{20}+\frac{4}{20}=\frac{7}{20} = \boxed{35\%} \end{aligned}