Hello, I'm having problems with statistics problems with multiple random variables

Hi, I'm CJ and I'm having issues with Probability and Statistics problems. Particularly the following type

If X[1] and X[2] are independent exponential random variables

with parameters lambda[1] and lambda[2] respectively, find the

distribution of Z=X[1] / X[2]. Also compute P(X[1] < X[2])

I'm guessing I need to find the distribution for F(Z) and then I can just find when that is less than 1. But I don't know how to do that. Any advice? Thanks!