Explanation

This is a conditional probability question that can be solved using Bayes' theorem or the basic conditional probability formula.

Given:

• Subprime mortgages: 2,500 total, with 500 late
• Prime mortgages: 800 total, with 64 late
• Total mortgages: 2,500 + 800 = 3,300
• Total late mortgages: 500 + 64 = 564

Step 1: Calculate the probability that a mortgage is late $P(\text{Late}) = \frac{564}{3300} = 0.1709 = 17.09\%$

Step 2: Calculate the joint probability of being subprime AND late $P(\text{Subprime} \cap \text{Late}) = \frac{500}{3300} = 0.1515 = 15.15\%$

Step 3: Apply conditional probability formula $P(\text{Subprime} | \text{Late}) = \frac{P(\text{Subprime} \cap \text{Late})}{P(\text{Late})} = \frac{0.1515}{0.1709} = 0.886 = 88.6\%$

Alternative direct approach: $P(\text{Subprime} | \text{Late}) = \frac{\text{Number of late subprime mortgages}}{\text{Total late mortgages}} = \frac{500}{564} = 0.886 = 88.6\%$

Rounding to the nearest whole percentage gives 89%, which corresponds to option D.

This result makes intuitive sense because subprime mortgages constitute a much larger portion of the portfolio (76% of total mortgages) and have a higher default rate (20% of subprime vs 8% of prime), so when we condition on a mortgage being late, it's very likely to be subprime.