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# What is the probability of getting a King and a Queen in TWO

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VP
Joined: 30 Sep 2004
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What is the probability of getting a King and a Queen in TWO [#permalink]  06 Mar 2005, 02:26
What is the probability of getting a King and a Queen in TWO draws of two cards from a pack of well-shuffled cards?
VP
Joined: 13 Jun 2004
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[#permalink]  06 Mar 2005, 06:03
I assume that 2 "draws" meaning is to get a king and a queen on both attempts or is it just on one ?

for both attempts

with the cards back into the game after the 1st attempt :
[(4*4)/(52*51)]^2

without any cards back after the first attempt:
[(4*4)/(52*51)]*[(3*3)/(50*49)] = (4*4*3*3)/(52*51*50*49)

For one attempt

if one time is sufficient out of the 2 attempts, and considering the attempt with the cards back after the 1st try, it should be : [(4*4)/(52*51)]*2

if one time is sufficient out of the 2 attempts, and considering the attempt without the cards back after the 1st try, it should be :
(4/52 * 4/51) + (3/50*4/49)+(3/50*4/49)+(4/50*4/49)

(4/52 * 4/51) -> if 1st try is enough
(3/50*4/49)+(3/50*4/49) -> you have to consider 2 special options : if during the 1st attempt a king has been picked but without a queen, and if a queen has been picked but without a king
(4/50*4/49) -> if during the 1st attempt no king and no queen has been picked

this is how i see it...
Senior Manager
Joined: 25 Oct 2004
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[#permalink]  06 Mar 2005, 15:19
4/52*4/51*3/50*3/49 (without replacement)

4/52*4/52*4/52*4/52 (with replacement)
[#permalink] 06 Mar 2005, 15:19
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# What is the probability of getting a King and a Queen in TWO

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