Question: b consider a cloud cluster of three servers the cluster...

(b)  Consider a cloud cluster of three servers. The cluster is considered available (or acceptable with a satisfactory performance level), if at least k servers are operating normally where k ≤ 3. Assume that each server has an availability rate of p (or a failure rate of 1 − p). Derive a formula to calculate the total cluster availability A (i.e., the probability that the cluster is available satisfactorily). Note that A is a function of k and p.

(c)  Given that each server has an availability p = 0.98, what is the largest minimum number of servers that must be available to achieve a total cluster availability A, which is higher than 96%? You have to check the effect of all possible values of k in part (b) in order to answer this question correctly