Explanation

This is a conditional probability problem. We need to find the probability that a beneficiary will receive a lump-sum payment given that they have already opted for monthly disbursements.

Given Data:

• Total beneficiaries: 100
• Monthly disbursements (A): 57
• Lump-sum payment (B): 43
• Both monthly and lump-sum (A ∩ B): 24

Applying Conditional Probability Formula:

$P(B \mid A) = \frac{P(A \cap B)}{P(A)}$

Where:

• $P(A \cap B) = \frac{24}{100} = 0.24$
• $P(A) = \frac{57}{100} = 0.57$

Calculation:

$P(B \mid A) = \frac{0.24}{0.57} = 0.4211 \approx 42\%$

Why Other Options Are Incorrect:

• A (24%): This is simply $P(A \cap B)$, the probability of both events occurring, not the conditional probability.
• C (50%): This appears to be an average of the two probabilities, not the correct conditional probability calculation.
• D (56%): This would be $P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.24}{0.43} \approx 56\%$, which is the reverse conditional probability (probability of monthly given lump-sum).

Therefore, the correct answer is 42%.