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JEE Main 20265 AprilEvening Shift
Exam
JEE Main
Year
2026
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2026 · 5 April · Evening Shift · Mathematics · Probability

The probabilities that players A and B of a team are selected for...

The probabilities that players AA and BB of a team are selected for the captaincy for a tournament are 0.60.6 and 0.40.4, respectively. If AA is selected the captain, the probability that the team wins the tournament is 0.80.8 and if BB is selected the captain, the probability that the team wins the tournament is 0.70.7. Then the probability, that the team wins the tournament, is :

Options

  1. A0.740.74
  2. B0.760.76
  3. C0.720.72
  4. D0.780.78

Correct answer

B. 0.760.76

Step-by-step solution

Let AA be the event that player A is selected as captain, and BB the event that player B is selected as captain. Let WW be the event that the team wins the tournament.

Given:
P(A)=0.6P(A) = 0.6, P(B)=0.4P(B) = 0.4
P(W∣A)=0.8P(W \mid A) = 0.8, P(W∣B)=0.7P(W \mid B) = 0.7

By the law of total probability:
P(W)=P(A)⋅P(W∣A)+P(B)⋅P(W∣B)P(W) = P(A) \cdot P(W \mid A) + P(B) \cdot P(W \mid B)

P(W)=(0.6)(0.8)+(0.4)(0.7)P(W) = (0.6)(0.8) + (0.4)(0.7)

P(W)=0.48+0.28=0.76P(W) = 0.48 + 0.28 = 0.76

Hence, the correct option is (2) 0.76(2)\ 0.76.
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