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...

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?