Answer-first summary for fast verification
Answer: 81%
## Explanation This is a conditional probability problem using Bayes' theorem. We need to find P(Subprime | Late). ### Given: - Total subprime mortgages: 1,000 - Late subprime mortgages: 200 - Total prime mortgages: 600 - Late prime mortgages: 48 - Total mortgages: 1,000 + 600 = 1,600 ### Step 1: Calculate total late mortgages Total late = Late subprime + Late prime = 200 + 48 = 248 ### Step 2: Apply Bayes' theorem P(Subprime | Late) = P(Late | Subprime) × P(Subprime) / P(Late) Where: - P(Late | Subprime) = 200/1,000 = 0.20 - P(Subprime) = 1,000/1,600 = 0.625 - P(Late) = 248/1,600 = 0.155 ### Step 3: Calculate the probability P(Subprime | Late) = (0.20 × 0.625) / 0.155 = 0.125 / 0.155 ≈ 0.8065 ≈ 81% Alternatively, we can use the direct approach: P(Subprime | Late) = Late subprime / Total late = 200 / 248 ≈ 0.8065 ≈ 81% Therefore, the probability that a randomly selected late mortgage is subprime is approximately **81%**.
Author: LeetQuiz .
Ultimate access to all questions.
An analyst is examining a portfolio that consists of 1,000 subprime mortgages and 600 prime mortgages. Of the subprime mortgages, 200 are late on their payments. Of the prime mortgages, 48 are late on their payments. If the analyst randomly selects a mortgage from the portfolio and it is currently late on its payments, what is the probability that it is a subprime mortgage?
A
60%
B
67%
C
75%
D
81%
No comments yet.