Machine $1$ is working now. Machine $2$ will be switched on at time $t$. Suppose that machine $1$ fails at rate $λ_1$ and $2$ at rate $λ_2$with an exponential waiting time. What is the probability that machine $2$ fails first?
It should be $P(X_2+t<X_1)$ or $P(X_2<X_1|X_2=t)$ but I don't know how to go about calculating it.
Can someone give me a hint?