Problem 2

1. When Alice gets stressed out about her classes, she plays agame in which she rolls a pair of dice and if the sum of the twonumbers is at least 10, she “wins.” For each win, she gives herselfa dollar for ice cream.

(a) The night before the final exam, Alice willplay this game 10 times. What is the probability that she will winherself at least $3 for ice cream?

(b) Alice teaches this game to Bob, who istaking another course. The night before his final exam, Bob playsthe game 10 times. But Bob really likes ice cream, and he’s reallystressed out, so he plays with a special pair of dice that areweighted so that p(5) = p(6) = 2p(4) = 2p(3) = 2p(2) = 2p(1). (Inother words, he is twice as likely to roll a 5 or a 6 than anyother number.) What is the probability that Bob will win himself atleast $3 for ice cream?

(c) How many times should Alice play her gameto ensure that she will have at least a 50% chance of winning atleast $5? (NOTE: Alice will play with the original version in (a)not Bob’s cheating version in (b).) (HINT: This may be rathertedious to calculate by hand, so you may want to write a shortprogram to calculate it. If you do, attach an image of your code aswell as a short explanation of your procedure and the finalanswer.)