George sets three alarm clocks. Each have a probability of 0.9 of going off at the correct time to wake him up for work. a) what is the probability that exactly 2 of them will go off at the correct time? b) what is the probability that at least one will go off at the correct time? c) If George has an old alarm clock with the probability of 0.6 of going off at the correct time, what is the minimum number of alarms needed to have a probability of at least 0.99 that at least one alarm clock will go off at the correct time?