A data center consists of 5 servers, S1, . . . , S5. Each server fails independently with probability p during the day. Failed servers are restarted at the end of each day. Give all of the following answers as a function of p - simplify the resulting expressions as far as possible.

a) What is the probability that S1 or S2 fails on a given day?

b) The data center remains operative as long as a server among {S1, S2, S3} is operative, and a server among {S3, S4, S5} is operative. What is the probability that the data center fails on a given day?