Recall that a poker hand consists of 5 cards chosen randomly

Recall that a poker hand consists of 5 cards chosen randomly from a standard 52 card deck. Find the probability that you are dealt a poker hand with precisely 2 queens. Find the probability that \"your hand is a pair of queens\", i.e. that (reordering if needed) your hand looks like (Q, Q, x, y, z) where Q is queen and the values Q, x. y, z are distinct. Find the chance that \"your hand is a pai\", i.e., that (reordering if needed) your hand looks like (x, x. y, z, w) where the values x, y, z, w are distinct. 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\" . Find an approximate value for the probability in the previous part.

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