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.
- A. 17/45
- B. 19/45
- C. 23/45 ✓
- 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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