Answer-first summary for fast verification
Answer: 81%
To solve this conditional probability question, we first calculate the probability that any one mortgage in the portfolio is late. This is calculated as follows: \[ P(\text{Mortgage is late}) = \frac{200 + 48}{1000 + 600} = \frac{248}{1600} = 15.5\% \] Next, we use the conditional probability relationship: \[ P(\text{Subprime mortgage | Mortgage is late}) = \frac{P(\text{Subprime mortgage and late})}{P(\text{Mortgage is late})} \] Since the probability that a mortgage is subprime and late is: \[ P(\text{Subprime mortgage and late}) = \frac{200}{1600} = 12.5\% \] We can then calculate the conditional probability: \[ P(\text{Subprime mortgage | Mortgage is late}) = \frac{12.5\%}{15.5\%} = 0.81 = 81\% \] Hence, the probability that a random late mortgage selected from this portfolio turns out to be subprime is 81%.
Author: LeetQuiz Editorial Team
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An analyst is evaluating 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 chooses a mortgage from the portfolio and it is currently late on it: payments, what is the likehood that it is a subprime mortgage?
A
60%
B
67%
C
75%
D
81%
