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Card Game Probability Question

Date: 5/22/96 at 15:21:51
From: Anonymous
Subject: Card Game Probability Question

Given a regular deck of 52 cards, what is the probability of getting 
the following combination: a spade, a queen, a diamond.  The cards 
taken are not to be placed back into the deck.

Date: 6/1/96 at 19:42:49
From: Doctor Anthony
Subject: Re: Card Game Probability Question

You can list the various ways that you can get a successful outcome:

(1) spade other than queen, queen of spades, diamond.  
    Prob = (12/52)(1/51)(13/50)

(2) spade, queen of hearts, diamond.  Prob = (1/4)(1/51)(13/50)

(3) spade, queen of diamonds, diamond.  Prob = (1/4)(1/51)(12/50)

(4) spade, queen of clubs, diamond.  Prob = (1/4)(1/51)(13/50)

Multiply these out and add them to give the total probability.

I get 1/204.

-Doctor Anthony,  The Math Forum
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Associated Topics:
High School Probability

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