In five-card poker games using a standard deck of 52 cards , a straight consists
ID: 2978042 • Letter: I
Question
In five-card poker games using a standard deck of 52 cards , a straight consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queens of spades, and King of clubs). Assume that aces can be high or low , and only "A2345" and "10JQKA" are counted (that is, "JQKA2" , "QKA23" and "KA234" are excluded). For a five-card hand, What is the probability that it will be a straight ? What is the probability that it will be a straight flush (all cards in the same suit)? Hint. First decide how many 5-cycles you can have totally, and then focus on one of them.Explanation / Answer
a. Start at ace as your first card and work your way up to 10. you can receive 4 different aces x 4 different 2's x 4 different 3's x 4 different 4's x 4 different 5's. this gives 4^5 possibilites for start with ace. Do the same up to 10, and you end up with 10 * (4^5) = 10240 to find the probability, you need to know the all possible combinations of any 5 cards, let that number be x. I assume you have calculated this somewhere else. then do 10240 / x b) similar to a, there are only ten ways to get a straight flush for each suit, so that gives a total of 40. 40 / x is your answer Hope this helps