There are $3$ new drink vending machines and $3$ new snack vending machines installed in a company. Suppose the lifetime (in years) of a drink vending machine is a $[0,5]$-uniform random variable, and the lifetime (in years) of a snack vending machine is a $[0,8]$-uniform random variable. The lifetimes of all the vending machines are independent. Find out the probability that after $4$ years there are exactly two vending machines still in work.
My first question is, are the variables continuous or discrete? At first I thought maybe it's discrete because it's in years, but couldn't a machine be working for, say, 2.5, or 1.75 years, therefore making it continuous? And if it is continuous, how would I find $P(X=4)$ assuming $x$ is the lifetime of the vending machine?
I've also found the PDFs and CDFs of the vending machines but I'm not sure where to go from there.