# Exam P Practice Problem 16 – Conditional Probability and Exponential Distribution

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Practice Problem 16A
Losses $X$ and $Y$ due to two different perils are independently and identically distributed according to the density function $f(x)=0.25 \ e^{-0.25 \ x}$ where $x>0$. If the total loss for the two perils is greater than $2$, what is the probability that $X$ is greater than $1$?

Practice Problem 16B
Losses $X$ and $Y$ due to two different perils are independently and identically distributed according to the density function $f(x)=0.125 \ e^{-0.125 \ x}$ where $x>0$. If the total loss for the two perils is greater than $6$, what is the probability that $X$ is less than $4$?

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