What is the probability that the bonus scheme will be introduced?

Consider the following for the two (02) items that follow : The probabilities that A, B and C become managers are 3/10, 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively.

  1. A. 17/45
  2. B. 19/45
  3. C. 23/45
  4. D. 26/45

Correct Answer: C. 23/45

Explanation

By the Law of Total Probability, P(\text{Bonus}) = P(A)P(\text{Bonus}|A) + P(B)P(\text{Bonus}|B) + P(C)P(\text{Bonus}|C). Substituting the given values, P(\text{Bonus}) = (3/10)(4/9) + (1/2)(2/9) + (4/5)(1/3) = 6/45 + 5/45 + 12/45 = 23/45.

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