A sample of n people includes Alfa and Bravo. A bootstrap sample (n draws at random with replacement) is drawn from the sample.

(a) [1pt] Find the probability that none of Alfa and Bravo is chosen in the bootstrap sample. Be careful about your use of the multiplication rule.

(b) [2pts] Find an approximated value of your answer in (a) when n is large enough. (Or equivalently, what happens to the result of your answer in (a) when n goes to )?

(c) [2pts] Suppose n people includes Alfa, Bravo, and Charlie. Repeat what you have done in (a) and (b): find the probability that none of these three is chosen; find an approximated value of your answer for large n