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Just need a help hand, I just want to know whether I'm doing the right thing for this question. A hand of 13 cards is to be dealt at random and without replacement from 52 cards. find the conditional probabilty that there are 2 kings given that the hand contains at least 3 kings. Let $X$ be the number of kings then $P( X\geq 2|X\geq 3) = 1 - P( X< 2|X\geq 3) $. Is it any independent problem ? An explanation will do..

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    Before going to formulas, it is useful to take a good look at the meaning of a question.2012-09-04

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If there are at least three kings, there are at least two kings. The probability is $1$.

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    And this problem is a perfect illustration of why one should **always** think about what’s going on before grabbing blindly for a handy formula!2012-09-04
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    @ Ross, how did you get 1?2012-09-04
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    @EugeneMettle: you are told that there are at least three kings in any case under consideration. We don't care how it was generated, the random and without replacement is extraneous information. Given that there are three kings, there **have** to be two, because two is less than three. If something has to be true, the probability is $1$.2012-09-04
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    A more interesting question would be what is the probability of getting three kings given that you got at least two. Maybe the OP got it turned around.2012-09-05