My Math Forum Probability with cards

 March 22nd, 2012, 09:01 PM #1 Newbie   Joined: Feb 2012 Posts: 10 Thanks: 0 Probability with cards Can someone please help me with this problem? Thank you! A 10-card hand is dealt from a standard deck of 52 playing cards. What is the probability that: a) you are dealt exactly 2 queens? b) you are dealt at most 3 diamonds?
 March 22nd, 2012, 09:35 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: Probability with cards There are ${52 \choose 10}$ possible hands. a) There are ${4 \choose 2}$ ways to choose 2 queens from 4 and ${48 \choose 8}$ ways to choose 8 cards from the remaining 48 to complete the hand. Thus, the probability P(A) of getting a hand with exactly 2 queens is: $P(A)=\frac{{4 \choose 2}\cdot{48 \choose 8}}{{52 \choose 10}}=\frac{1107}{7735}$ b) Using the method above, we find: $P(B)=\frac{{13 \choose 1}\cdot{39 \choose 9}+{13 \choose 2}\cdot{39 \choose 8}+{13 \choose 3}\cdot{39 \choose 7}}{{52 \choose 10}}=\frac{2458391}{3253810}$

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