贝叶斯

问题如下：

A risk manager at a civil service pension scheme is conducting a year-end review on the disbursement preferences of 100 retirement plan beneficiaries and observes the following:

ü 57 beneficiaries have opted to receive monthly disbursements.

ü 43 beneficiaries have opted to receive a lump-sum payment.

ü In addition, 24 of the beneficiaries that have opted to receive monthly disbursements will also receive a lump-sum payment after a period of time.

If a retirement plan beneficiary selected at random from this sample has opted for monthly disbursements, what is the probability that the beneficiary will also receive a lump-sum payment?

选项：

A.

24%

B.

42%

C.

50%

D.

56%

解释：

Recall that for conditional probabilities, P(A | B) = P(A ∩ B) / P(B).

Thus, if we set

A = opted for monthly disbursements

B = opted for a lump-sum payment

P(B | A) = P(B ∩ A) / P(A) = 0.24/0.57 = 0.4211 or approx. 42%

A is incorrect. This is just P(B ∩ A).

C is incorrect. This is the average of P(A) and P(B).

D is incorrect. This is the value of P(B ∩ A) / P(B).