A ski resort has four snowmobiles that the ski patrol uses.Each machine starts in the morning 90% of the time without any help from the resort mechanic.(Assume each machine starts or does not start independently of the others.)If all four machines start, the mechanic can get an extra hour of sleep in the morning.If any of the machines will not start, the mechanic loses out on the extra hour of sleep and must spend 15 minutes starting each machine that would not start and spend the remainder of the hour drinking coffee.If only one machine will not start, the mechanic will get it going in 15 minutes and spend the other 45 minutes drinking coffee.

a)What is the probability that the mechanic can sleep in for an hour?

b)What is the probability that the mechanic will lose the extra hour and have only 15 minutes for coffee?

c)What is the probability that the mechanic will drink coffee for exactly half an hour?

d)What is the probability that the mechanic will have at most 30 minutes for coffee? (Assume the extra hour of sleep the mechanic might get is equivalent to an hour for coffee, he just chooses to sleep instead of drink coffee.)