Let X,Y be independent exponential (1) random variables. a. Compute the conditional probability that X < In

Question:

Let X,Y be independent exponential (1) random variables.
a. Compute the conditional probability that X < In 2, given X - Y ≥ 0. In other words, find
P(X < In 2 | X -Y ≥ 0).
b. Compute the conditional probability that X < In 2, but now given X - Y is exactly 0. In other words, find
P(X < In 2 | X -Y = 0).