Suppose that the amount of time between consecutive surges in an electricity network has an exponential distribution with rate of one surge every nine days. (a) What is the probability that exactly two power surges occur in the next eight days? (b) What is the probability that the next power surge happens at least five days from now? (c) What is the probability that at most four power surges occur in the next ten days? (d) What is the probability that the next power surge takes place four to six days from now? (e) What is the probability that the next power surge will occur less than fifteen days from now, given knowledge that the next power surge will not occur within the next three days?

Is the answer to a not 0.1624 and b 0.5738?