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 March 27th, 2011, 06:50 PM #1 Newbie   Joined: Mar 2011 Posts: 1 Thanks: 0 Deck of Cards Probability You are dealt 4 cards from a standard deck of cards. What is the probability you get a 4 card straight, in a black suit, starting with Jack and ending with Ace?
 March 27th, 2011, 06:57 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Deck of Cards Probability There are only two such hands, one in clubs and one in spades. The total number of 4 card hands is: $\binom{52}{4}=270725$ thus the probability is $\frac{2}{270725}$
March 27th, 2011, 07:23 PM   #3
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Re: Deck of Cards Probability

Quote:
 Originally Posted by MarkFL There are only two such hands, one in clubs and one in spades.
We are looking for straights, not flushes.

$\frac{8}{52}\,\cdot\,\frac{6}{51}\,\cdot\,\frac{4} {50}\,\cdot\,\frac{2}{49}\,=\,\frac{16}{270725}$

 March 27th, 2011, 07:28 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Deck of Cards Probability Ah yes, big difference between a straight and a straight flush!! You're right, there are $2^4$ such hands. Thanks for catching that flub!

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