Compute the probabilities for the following situations. These probabilities can be computed analytically, or you may write a computer program to generate the probabilities by simulation.
(a) Out of a group of 23 students, what is the probability that 2 students share the same birthday?
(b) Out of a group of 100 students, what is the probability that 3 students share the same birthday?
(c) How many students must be in the class for the probability to be at least 50% that there are 2 who share a birthday in the same month?