The question is asking for the conditional probability that a retirement plan beneficiary, selected at random from the sample, will also receive a lump-sum payment given that they have opted for monthly disbursements. The correct answer is B, which is 42%.

The explanation for this answer is based on the concept of conditional probability. Conditional probability is calculated using the formula P(A | B) = P(A ∩ B) / P(B), where P(A | B) is the probability of event A occurring given that event B has occurred, P(A ∩ B) is the probability of both events A and B occurring together, and P(B) is the probability of event B occurring.

In this scenario:

• Event A is the beneficiary opting for monthly disbursements.
• Event B is the beneficiary opting for a lump-sum payment.

From the data provided:

• There are 57 beneficiaries who opted for monthly disbursements (P(A) = 57/100).
• There are 43 beneficiaries who opted for a lump-sum payment.
• There are 24 beneficiaries who have opted for both monthly disbursements and a lump-sum payment (P(A ∩ B) = 24/100).

Plugging these values into the formula for conditional probability: P(B | A) = P(A ∩ B) / P(A) = (24/100) / (57/100) = 24/57 ≈ 0.4211, which is approximately 42%.

This calculation shows that if a beneficiary has opted for monthly disbursements, there is a 42% chance that they will also receive a lump-sum payment.