A train from Ottawa to Montreal is scheduled to arrive at 9 am every weekday morning. The probability that the train arrives on time is 0.90. Suppose 15 weekdays are randomly selected.

(a) Find the probability that the train will arrive on time at most 10 days.

(b) Find the probability that the train will arrive on time at least 12 days.

(c) Find the expected number of days that the train will arrive on time.

(d) Suppose the train arrives on time on at least 10 days. What is the probability that it arrives on time on all 15 days?