Given drawing the indicated cards from a standard 52 card deck; write the probability as an expression rather than numerically evaluating it. 3.1 The second of two cards is a heart. 3.2 Five cards, of a same suit. 3.3 Five cards, none of which is heart 3.4 Four cards of the same face and one card of a different face. 3.5 Four hearts and one none heart. 3.6 Two pairs of cards, the pairs having a different face, and a card with a face different from both pair.
Given drawing the indicated cards from a standard 52 card deck; write the probability as an expression rather than numerically evaluating it. 3.1 The second of two cards is a heart. 3.2 Five cards, of a same suit. 3.3 Five cards, none of which is heart 3.4 Four cards of the same face and one card of a different face. 3.5 Four hearts and one none heart. 3.6 Two pairs of cards, the pairs having a different face, and a card with a face different from both pair.
Given drawing the indicated cards from a standard 52 card deck; write the probability as an expression rather than numerically evaluating it. 3.1 The second of two cards is a heart. 3.2 Five cards, of a same suit. 3.3 Five cards, none of which is heart 3.4 Four cards of the same face and one card of a different face. 3.5 Four hearts and one none heart. 3.6 Two pairs of cards, the pairs having a different face, and a card with a face different from both pair.
3.1. The first can either be a heart or a non-heart. If it is a heart, then the probability that the second of 2 cards is a heart is 13/52 x 12/51 = 1/4 x 12/51. If it is a non-heart, then the probability that the second of 2 cards is a heart is 39/52 x 13/51 = 3/4 x 13/51.
Therefore, the probability that the second of 2 cards is a heart is = 1/4 x 12/51 + 3/4 x 13/51 = (12 + 3 x 13)/(4 x 51)
3.2 Probability of 5 cards of 1 suit = 13/52 x 12/51 x 11/50 x 10/49 x 9/48.
Since there are 4 suits, probability of Five cards, of a same suit = 4 x 13/52 x 12/51 x 11/50 x 10/49 x 9/48.
3.3 Probability of Five cards, none of which is heart = 39/52 x 38/51 x 37/50 x 36/49 x 35/48
3.4 Probability of Four cards of the same face and one card of a different face = 4/52 x 3/51 x 2/50 x 1/49
Since there are 13 faces, probability of Four cards of the same face and one card of a different face = 13 x 4/52 x 3/51 x 2/50 x 1/49
3.5 Probability of Four hearts and one none heart. = 13/52 x 12/51 x 11/50 x 10/49 x 39/48
3.6 Probability of Two pairs of cards, the pairs having a different face, and a card with a face different from both pair. = 13 x 4/52 x 3/51 x 4/50 x 3/49 x 44/48
Homework Sourse
