为什么这道题是求条件概率而不是joint probability呢

问题如下：

An analyst estimates that the hazard rate for a company is 0.16 per year. The probability of survival in the first year followed by a default in the second year is closest to:

选项：

A.

11.62%

B.

13.63%.

C.

14.79%

D.

27.39%

解释：

Explanation: The probability that the firm defaults in the second year is conditional on its surviving the first year. Using λ to represent the given hazard rate, we can calculate the cumulative probability of default in the first year using the formula 1– exp(–1*λ) = 1 – exp(-0.16) = 0.14786. Thus, probability of survival in the first year = 1 – 0.14786 = 0.85214.

Then, the cumulative probability that the firm defaults in the second year = 1 – exp(–2*λ) = 1 – exp(-2*0.16) = 0.27385, and the conditional one year default probability given that the firm survived the first year is the difference between the two year cumulative probability of default and the one year probability divided by the probability of survival in the first year = (0.27385 – 0.14786)/0.85214 = 0.14785 = 14.79%.