In poker you have 7 cards toplay with and you make your best 5 card hand from th
ID: 2955178 • Letter: I
Question
In poker you have 7 cards toplay with and you make your best 5 card hand from those 7cards. The deck has 52 cards in it, with 13 of each of spades,hearts, diamonds, and clubs. You hold
a “flush" if you have at least 5 cards of the same suit.
(a) Calculate the probability that you are dealt a flush (we talkedabout how to do this in class,
begin by calculating the proabability of a flush for a particularsuit and work from there).
(b) Note that what you just calculated includes straight flushes(that is, flushes for which at least
5 of the suited cards happen to be in order). What is theprobability of a drawing a flush that
is not a straight flush? (Note: each suit has cards A, 2, 3, 4, 5,6, 7, 8, 9, T, J, Q, K where A =
ace and T = ten. Straight flushes include both the sequence A2345and TJQKA but not other
sequences in which cards “wrap around" such as QKA23).
Explanation / Answer
pick clubs for flush We need 5 from 13, c(13,5) The other two cards are from remaining cards(52-5=47),C(47,2) number of club flushes =C(13,5)*C(47,2) coulb be any of 4 suits total number= 4C(13,5)*C(47,2)=556498 number of hands 7 cards from deck of 52 cards C(52,7) Probability of flush= 556498/C(52,7) = .0041597 B) straight flush could start with A,2,3,...T 10 choices for first card in sequence 4 choices for suit of straight flush Number of straight flush=4*10 since we are still drawing 7 cards the last two could be anythingleeft in deck (47), C(47,2) Number of straight flushes of 5 cards when dealt 7 =40*1081=43240 Number of flushes not straight flushes= 556498-43240=513258 Probability of above (answer)=.003836