# math

using a deck of cards,what is the probability that you would pull a red kind and a black queen in two pulls without replacing the first card back into the deck?

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1. I believe you mean read KING, not red KIND. There are two red kings and two black queens. The probability of drawing either one, in a single draw, is 2/52 = 1/26.
There are two ways you could end up with one black queen and one red king: You could get the king first or the queen first. The total probability is
2*(1/26)^2 = 1/338

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posted by drwls
2. Since you are not replacing the card, the prob of the second draw is different from the first draw.

could be RK,BQ or BW,RK
prob of that is (2/52)(2/51) + (2/52)(2/51)
= 2(2/52)(2/51) = 2/663

or

choose a red king -->C(4,2) = 2
choose a black queen --> C(4,2) = 2
choose any two cards --> C(52,2) = 1326
prob = 2*2/1326 = 2/663

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posted by Reiny
3. Reiny is correct; I missed the word "without" (replacing).

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posted by drwls

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