A store sells three types of candies, lollipops, tootsie rolls and gummy bears. A customer purchases lollipops with probability 0.6, tootsie rolls with probability 0.3 and gummy bears with probability 0.1. Now five customers come to purchase candies in a queue and their decisions are independent with each other.

(a) What is the probability that two customers purchase lollipos, two customers purchase tootsie rolls and one customer purchases gummy bears?

(b) What is the probability mass function of the number of customers who purchase gummy bears?

(c) What is the mean and variance of the number of customers who purchase gummy bears?

(d) Assume the five customers are your friends and you play a little game with them. You make the guess that all of them will buy lollipops but they don't know the guess. For each of your friend, if your guess is wrong, you will pay her(him) $5. If your guess is right, your generous friend will pay you $10. What is the expected amount of money you will make in this game?

(e) What is the probability that the last two customers purchase gummy bears, given that the first two customers purchase gummy bears?

(f) What is the probability that two customers purchase gummy bears, given that two customers purchase tootsie rolls?

I know its alot of parts... sorry i will definitly give a positive rating if ans. seem correct