2. In a game called five-card draw poker, each player receives 5 cards (called a hand) taken at random from a standard deck of 52 cards. Each card in the deck has a rank (in order A, 2, 3, 4, 5, 6, 7, 8, 9, 10, I, Q, K) and a suit (in no particular order, Q), 0, in, Q). Some possible hands in this game are summarized in Table 1 belowl. (a) Describe the sample space S for the experiment of receiving a poker hand (the order you receive the cards does not matter in this game). Determine the cardinality of S. (b) Let E be the event that the hand contains at least two cards of the same rank and F be the event that the hand contains at least three cards of the same rank. The cards you got in the rst round are mathematically described by the event E 0 F. What are the possible hands (from Table 1) that you could be playing with? (c) Repeat (b), but now with E U P. (d) Repeat (b), but now with E \\ F. 1Note that the A is the only card that can take two positions in the ranking: it can go before the 2 as above or after the K. You may also find a precise description of the poker hands at https : //en.wikipedia. org/wiki/List_of _poker_hands. Hand Explanation Example Royal ush Five cards of the same suit in sequence 10%, Ida, Q, K, Ad. Four of a kind All four kinds of the same rank 4% 40, 4Q, 4*, IQ? Full house Three of a kind with a pair 70, 7*, 7+, 3.1., 35? Plush Any ve cards of the same suit, not in sequence 3'3, AW, 29, KC), 10?? Straight Five cards in sequence, not all of the same suit 7.1., 8-1., 9.1-, 100, IQ Three of a kind Exactly three cards of the same rank K0, K5, KQ, A&, (2.7. Two pair Two different pairs 19, Ho, 60, 61., A0 One pair One pair of the same rank [(33, I13, 91-, (2*, AG High hand None of the above, plays with highest card 20, 8?), 10.1., Ki, A Table 1: Standard poker hands, from strongest to weakest