Answer: 89%

## 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.

Author: LeetQuiz .