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4. In one variety of poker, players are dealt five cards from an ordinary deck of 52 cards.
(a) A full house in poker is a hand of five cards of one denomination and 3 cards of another denomination. Find the probability of a player being dealt a full house.
(b) Two pairs is a poker hand containing 2 cards of one denomination, another 2 cards of a second denomination, and a fifth cards of a third dimension. Find the probability of a player being dealt two pairs.
5. Given n marbles where k of the marbles are black and the rest are white, a game is played as follows. You choose two marbles at random, and you win the game if the marbles are of different colors. Prove that for a fixed n, you have the highest probability of winning when k = n/2 (for even values of n) and when k = (n (plus or minus) 1)/2 (for odd values of n)
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MATH1550H: Assignment: Questions: Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.
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