The probabilities that players A and B of a team are selected for captaincy are 0.6 and 0.…

Question

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

Accepted Answer

$P(A)=0.6,\ P(B)=0.4$; $P(W\mid A)=0.8,\ P(W\mid B)=0.7$.

$$P(W) = P(A)P(W\mid A)+P(B)P(W\mid B) = 0.6\times0.8+0.4\times0.7 = 0.48+0.28=0.76$$

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