ProbabilityMedium

Question

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 :

Options

A.0.74
B.0.76
C.0.72
D.0.78

Solution

Sol. [Key Concept: Total winning probability $= P(A)P(winmid\ A) + P(B)P(winmid\ B)$.]

$P($ Win $) = P(A \cap$ Win $) + P(B \cap$ Win $)$

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

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