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MathEasyMain 2026 • 5th Apr - Shift 2

Find Probability Team Wins Tournament Given Captain Probabilities

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.60.6 and 0.40.4, respectively. If A is selected the captain, the probability that the team wins the tournament is 0.80.8 and if B 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

A

0.740.74

B

0.760.76

Correct
C

0.720.72

D

0.780.78

Topics & Concepts

ProbabilityProbabilityConditional ProbabilityBayes' Theorem

Step-by-Step Solution

To find the total probability that the team wins the tournament, we can use the Law of Total Probability.

Let the events be defined as follows:

  • CAC_A: Player A is selected as the captain.
  • CBC_B: Player B is selected as the captain.
  • WW: The team wins the tournament.

From the given information:

  • The probability that A is selected as captain, P(CA)=0.6P(C_A) = 0.6
  • The probability that B is selected as captain, P(CB)=0.4P(C_B) = 0.4
  • The conditional probability that the team wins given A is the captain, P(W∣CA)=0.8P(W \mid C_A) = 0.8
  • The conditional probability that the team wins given B is the captain, P(W∣CB)=0.7P(W \mid C_B) = 0.7

By the Law of Total Probability, the total probability that the team wins the tournament, P(W)P(W), is given by: P(W)=P(CA)⋅P(W∣CA)+P(CB)⋅P(W∣CB)P(W) = P(C_A) \cdot P(W \mid C_A) + P(C_B) \cdot P(W \mid C_B)

Substituting the given values into the formula: P(W)=(0.6×0.8)+(0.4×0.7)P(W) = (0.6 \times 0.8) + (0.4 \times 0.7) P(W)=0.48+0.28P(W) = 0.48 + 0.28 P(W)=0.76P(W) = 0.76

Thus, the probability that the team wins the tournament is 0.760.76.

Correct Option: B (0.760.76)

Find Probability Team Wins Tournament Given Captain Probabilities | Mathematics PYQ Solution - JEE Challenger