能不能这么算？

问题如下：

An analyst is examining a portfolio that consists of 600 subprime mortgages and 400 prime mortgages. Of the subprime mortgages, 120 are late on their payments. Of the prime mortgages, 40 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?

选项：

A.

60%

B.

67%

C.

75%

D.

80%

解释：

In order to solve this conditional probability question, first calculate the probability that any one mortgage in the portfolio is late. This is: P(Mortgage is late) = (120 + 40)/1000 = 16%.

Next use the conditional probability relationship as follows:

P (Mortgage subprime | Mortgage is late) = P(Mortgage subprime and late) / P(Mortgage is late)

Since P(Mortgage subprime and late) = 120/1000 = 12%;

Therefore P(Mortgage subprime | Mortgage is late) = 12% / 16% = 0.75 = 75%.

Hence the probability that a random late mortgage selected from this portfolio turns out to be subprime is 75%.