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From an ordinary deck of cards, only 12 picture cards are

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Manager
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From an ordinary deck of cards, only 12 picture cards are [#permalink] New post 11 Jun 2007, 09:16
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From an ordinary deck of cards, only 12 picture cards are retained. They are shuffled (mixed) and a man draws 2 cards at random and announces that he holds at least one king. Find the probability that he holds two kings in his hand.


(A) 3/11 (B)4/11 (C)2/9 (D)6/13 (E)3/4
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 [#permalink] New post 11 Jun 2007, 09:22
Once the guy has pulled out 1 king, there are 11 cards left. Out of which 3 are kings. So the probability of 2 kings is 3/11.

Option A.
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 [#permalink] New post 11 Jun 2007, 12:36
Im getting some weird answer:

If he says he has atleast one king, then he has either 1 king, or 2 kings.

So, probability of having 2 kings given he has atleast 1 is:

4c2*8c0 / ( 4c2*8c0 + 4c1*8c1) = 3/19

This isn't even an option :shock:
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 [#permalink] New post 12 Jun 2007, 20:08
bsd_lover wrote:
Once the guy has pulled out 1 king, there are 11 cards left. Out of which 3 are kings. So the probability of 2 kings is 3/11.

Option A.
Huh?

4/12 * 3/11 = 1/11. How'd you figure it?
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 [#permalink] New post 12 Jun 2007, 20:19
Yes, that is correct. But the question is phrased in a way that shows that the event of first card being a king has already occured. So you dont need to multiply 3/11 by 4/12. 3/11 should be sufficient.

What is the OA ?
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 [#permalink] New post 12 Jun 2007, 21:32
Yeah, the caveat here is him stating that he has one king. If we do not have to calculate the probability of him bluffing into the situation, we can assume that there is a 100 percent chance that he holds a king.

All we need to do is calculate the probability that the next card is a king. In this case 3/11.
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 [#permalink] New post 13 Jun 2007, 06:57
We have 12 cards out of which 4 are kings.

Since we know that one king has been drawn, only three are left.
So the probability of having two kings is the probability of drawing a king out of group of 11 cards that includes 3 kings.

So P(2 kings)= 3/11
  [#permalink] 13 Jun 2007, 06:57
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