Suppose that there are 30 people in your statistics class and you are divided into 15 teams of 2 students each. You happen to mention that your birthday was last week, upon which you discover that your teammate's mother has the same birthday you have (month and day, not necessarily year). Assume that the probability is 1/365 for any given day.
a. What is the probability that your teammate's mother would have the same birthday as yours?
b. Suppose that your teammate has two siblings and two parents, for a family of size five. What is the probability that at least one of your teammate's family has the same birthday as yours, assuming their birth dates are all independent?
c. Is the fact that your teammate's mother has the same birthday as yours a surprising coincidence? Explain.