Question

1. A hand of four cards is drawn from a standard deck of 52 playing cards (without re- placement). Determine the probability that the hand contains: (a) four cards of the same value. (e.g. 20, 24, 26, 20). (b) two cards of one value and two cards of another value. (e.g. 3º, 2º, 24, 30) (c) four cards of the same suit. (e.g. 4♡, 2V, AV, K♡). (d) exactly two Queens. (e.g. KV, 36, QO, Qob) (e) exactly three spades. (e.g. AA,364, J4,34) (f) three cards of one suit and one card of another suit. (e.g. 26, 34, 64, K of)

Answer 1

We have 13 sets (a) P[ four cards ir same values four same of some vale 52.51.50 Ag 14x51x50x49) 499800 20825 TOP/2 cards of one value & cards of amolar value] (3)x(1) (3) 2808x4! - 2808 52.51.50.49 6497400 270725 41 Since we have 13 sets of 4 same values we can choose any 2 out 13 sets and from each set we can choose 2 cards. (c) P[ 4 cards of same suits] (1) (1) - 286084! 2860 52 51 50 49 6497400 270725 46 we have 4 suits and each suit has 13 cards so out of 13 we can choose 4 cards of name suits and also a different suits are available

48 (d) Pl Exactly 2 Queens] - (1) (2) 6768 (52) 270725 oud of & Queens 2 are to be chosen and from the rest 48 cards 2 cards are to closen. (e) Pl exactly 3 spades] - (3) () 1154 270725 111S 4 52 out of 13 spades 3 are to chosen and from rest (32-13) 39 cards is chosen 152 (+ PL 3 cards are from 1 suit] (6) () () 22308 22308 (5) 270725 out of 4 suits, choose 2 suits and then from one suit of 13 cards choose a cards and from another suit of 13 cards choose 1. 182) 152.51 50 49 )