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Maths Question 8 – JEE-MAIN 2026

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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:

Define the relevant events for captain selection and winning the tournament.

Step 1: Define Events and Given Probabilities✦ Active

Let A be the event that player A is selected as captain, and B be the event that player B is selected as captain. Let W be the event that the team wins the tournament. From the problem statement, we are given:

P(A)=0.6 P(B)=0.4 P(W|A)=0.8 P(W|B)=0.7
Step 2: Apply the Law of Total Probability○ Expand

Since events A and B are mutually exclusive and exhaustive (as P(A)+P(B)=0.6+0.4=1.0), we can use the Law of Total Probability to find the probability that the team wins the tournament, P(W).

P(W)=P(W|A)P(A)+P(W|B)P(B)
💡 Teacher's Secret Hint

Ensure that the events forming the partition are indeed mutually exclusive and exhaustive before applying the formula.

Step 3: Calculate the Result○ Expand

Substitute the given values into the formula:

P(W)=(0.8)(0.6)+(0.7)(0.4)P(W)=0.48+0.28P(W)=0.76

The probability that the team wins the tournament is 0.76.

💡 Teacher's Secret Hint

Double-check your arithmetic to avoid calculation errors.

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