Consider a computer system which employs two copies $A$ and $B$ of some chip. A chip $C$ on reserve is used to replace either $A$ or $B$ whichever fails first. What is the probability that $A$ is still in service after the other two have failed when:
(a) the lifetime of each chip is exactly 10 minutes.
(b) the lifetime are $i (i= 1,2,3)$ with probability 1/3.
(c) the lifetimes are exponential with mean $1/\mu$.
I guess the answer is somehow related to the properties of Poisson process and cannot figure out how. Any help is useful. Thanks!