Q1) Let 3 trails (they may not be independent), each of which is either success or not. Let X denotes number of successes. Assume E[X] = 1.8

a) Determine the largest possible value of P(X=3)?

b) Determine the smallest possible value of P(X=3)?

Q2) Airline knows that 5% of people making reservations on certain flight will not show up. Therefore, their policy is to sell 52 tickets for flight which can only hold 50 passengers. Determine the probability that there will be a seat available for every passenger who shows up?

Q3) A gambler has a fair coin and a two-headed coin in his pocket. He chooses one of the coins at a random, and when he flips it, it shows heads.

a)  Determine the probability that it is a fair coin?

b) Assume that he flips same coin a second time and again it shows heads. Now determine the probability that it is a fair coin?