could you please explain the steps up to reach the solution below

9. Suppose that the amount of claims from two insurance policies are denoted as X and Y and suppose that X ~ uniform(0, 2) and Y ~ uniform (0, 1) are independent, Le. the density function for X is f(a=)=, 05232; and the density function for Y is f(y)=l, OSysl- The insurance company hopes that the total amount of claims will not exceed 0.5, otherwise the company will get mined. What is the probability that the total amount of claims is less than 0.5? Solution P(X + Y S 05) = P(X 5 0.5 Y) = E {P(X s 0.5 Y|Y)| E %(0.5 Y) ID" 5 0.5] = 0.125 0.5E(YI[Y 5 0.51)) = 0.125 - 0.0625 = 0.0625