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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 :

Options

  1. A0.74
  2. B0.76
  3. C0.72
  4. D0.78

Correct answer

B. 0.76

Step-by-step solution

Let A be the event that player A is selected as captain, and B the event that player B is selected as captain. Let W be the event that the team wins the tournament. Given: P(A) = 0.6 , P(B) = 0.4 P(W A) = 0.8 , P(W B) = 0.7 By the law of total probability: P(W) = P(A) P(W A) + P(B) P(W B) P(W) = (0.6)(0.8) + (0.4)(0.7) P(W) = 0.48 + 0.28 = 0.76 Hence, the correct option is (2) 0.76 .

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