# Suppose a deck of 52 cards is shuffled the top card

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Problem 1.2Suppose a deck of 52 cards is shuffled. The top card is dealt. The dealt card isplaced back in the deck and the deck is shuffled again. Once again, the top card is dealt. (i.e., Atotal of two cards were dealt, where each dealt card was equally likely to be one of 52 cards.)(a) How many ordered pairs of cards could possible result as outcomes?Assuming each of these pairs has the same chance, calculate:(b) the probability that the first card is an ace.(c) the probability that the second card is an ace.(d) the probability that both cards are aces.(e) the probability at least one of the cards is an ace.
Problem 1.3Suppose two fairn-sided dice are rolled.Find the probabilities of the followingevents:(a) the maximum of the two numbers rolled is less than or equal to 2.(b) the maximum of the two numbers rolled is less than or equal to 3.(c) the maximum of the two numbers is exactly equal to 3.(d) the maximum of the two numbers rolled is less than or equal to 5.(e) the maximum of the two numbers is exactly equal to 5.
MATH/STAT 230 Homework 13(f) Denote byP(x) the probability that the maximum number is exactlyx. Find
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