A poker hand consists of 5 cards chosen randomly from a standard 52 card deck.
a) Find the chance that you are dealt a poker hand with exactly 2 aces.
b) Find the chance that your hand is a pair of Aces", i.e., that your hand looks like (A; A; r; s; t), where the values r; s; t are distinct from each other and from A.
(Hint: start by conditioning on the event in the previous part.)
c) Write an exact formula (in terms of some binomial distribution) for the probability that you get your 150th one pair" on or after the 400th deal" .
(Note: In this question you should use p to denote the probability of one pair rather than a numerical value)