IIM-K (BMSAT) 2025 (QA) PYQs

Given below are two statement based on the following

If $A$ and $B$ are independent events such that $P(A)=p, P(B)=2 p$ and $P$ (exactly one of $A, B)=\frac{5}{9}$

Statement I: $\mathrm{p}=\frac{1}{3}$

Statement II: $\mathrm{p}=\frac{5}{12}$

In the light of the above statements, choose the correct answer form the question given below

A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is

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?