Mathematics · Probability

JEE Main 2026 — 5 April, Evening Shift — Question 32

The probabilities that players A and B of a team are selected for the captaincy for a tournament are $0.6$ and $0.4,$ respectively. If A is selected the captain, the probability that the team wins the tournament is $0.8$ and if B is selected the captain, the probability that the team wins the tournament is $0.7.$ Then the probability that the team wins the tournament is :

Option A:
$0.74$
Option B:
$0.76$
Correct
Option C:
$0.72$
Option D:
$0.78$

Answer: B

Step-by-step solution

$\mathrm{P}($ Win $)=\mathrm{P}(\mathrm{A} \cap$ Win $)+\mathrm{P}(\mathrm{B} \cap$ Win $)$

\begin{aligned} & =\mathrm{P}(\mathrm{~A}) \cdot \mathrm{P}\left(\frac{\text { Win }}{\mathrm{A}}\right)+\mathrm{P}(\mathrm{~B}) \cdot \mathrm{P}\left(\frac{\text { Win }}{\mathrm{B}}\right) \\& =(0.6)(0.8)+(0.4)(0.7) \\& =0.48+0.28=0.76 \end{aligned}

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 5 April, Evening Shift
Subject: Mathematics
Chapter: Probability
Topic: Conditional Probability and Multiplication Theorem