1. (The birthday problem)Suppose there areCpeople, each of whose birthdays (month and day only) are equally likely to fall on any of the 365 days of a normal (i.e., non-leap) year.

a ) - SupposeC=2. What is the probability that the two people have the same exact birthday?

b ) - SupposeC2. What is the probability that allCpeople have the same exact birthday?

c) - SupposeC2. What is the probability thatsome pairof theCpeople have the same exact birthday? (Hint: You may wish to use (1.3.1).)

d ) - What is the smallest value ofCsuch that the probability in part (c) is more than 0.5? Do you find this result surprising?