If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?
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. 5/23 ✓
- B. 6/23
- C. 7/23
- D. 8/23
Correct Answer: A. 5/23
Explanation
Using Bayes' Theorem, P(B|\text{Bonus}) = \frac{P(B)P(\text{Bonus}|B)}{P(\text{Bonus})}. From the previous calculation, P(B)P(\text{Bonus}|B) = (1/2)(2/9) = 1/9 = 5/45 and total P(\text{Bonus}) = 23/45. Thus, the required probability is 5/23.
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