3 individuals John Wright, Greg Chappell and Gary Kristen are in the race for…

202520242023

3 individuals John Wright, Greg Chappell and Gary Kristen are in the race for the appointment of new coach of team India. The probabilities of their appointment are 0.5, 0.3, 0.2 respectively. If John Wright is appointed then probability of Ganguly appointed as a Captain will be 0.7 and the corresponding probability if Greg Chappell or Gary Kristen is appointed are 0.6 or 0.5 respectively. Find the overall probability that Ganguly will be appointed as a Captain ?

  1. A.

    0.18

  2. B.

    0.35

  3. C.

    0.63

  4. D.

    0.89

Attempted by 4 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

To find the overall probability that Ganguly is appointed as Captain, we need to consider all possible scenarios (which coach is appointed) and calculate the probability of Ganguly being appointed in each case.

  1. Define the Events:

    • P(J) = Probability John Wright is appointed = 0.5

    • P(G) = Probability Greg Chappell is appointed = 0.3

    • P(K) = Probability Gary Kristen is appointed = 0.2

    • P(C|J) = Probability Ganguly is appointed given John is coach = 0.7

    • P(C|G) = Probability Ganguly is appointed given Greg is coach = 0.6

    • P(C|K) = Probability Ganguly is appointed given Gary is coach = 0.5

  2. Apply Law of Total Probability: The overall probability P(C) is the sum of the probabilities of each mutually exclusive path: P(C) = [P(J) * P(C|J)] + [P(G) * P(C|G)] + [P(K) * P(C|K)]

  3. Calculate each path:

    • John's path: 0.5 * 0.7 = 0.35

    • Greg's path: 0.3 * 0.6 = 0.18

    • Gary's path: 0.2 * 0.5 = 0.10

  4. Sum the results:

    • 0.35 + 0.18 + 0.10 = 0.63

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