Suppose you are dealt a $5$-card hand from a standard deck, and that your hand has $1$ ace and $1$ queen. What is the probability that your hand has only one suit? two suits? three suits? four suits?
Probability of # of suits dealt given that your hand must have one ace and one king.
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0The discrepancy between the title and the body of the question creates ambiguity. The title seems to imply that the king's suit is included in the suit count, whereas the body seems to imply that it isn't. Also, the title appears to ask for a conditional probability, whereas the body appears to ask for the probability of the intersection of events, without conditioning. Please clarify. – 2012-11-01
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0Write clearly and in complete sentences. Phrase your question as a question. – 2012-11-01
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0I wondering about the conditional probability. Clarification: what is the probability that the number of suits in the hand is 1 given the hand has a king. What is the prob that the number of suits in the hand is 2 given the hand has a king. What is the prob that the number of suits in the hand is 3 given the hand has a king. What is the prob that the number of suits in the hand is 4 given the hand has a king. – 2012-11-01
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0If x=the # of suits in the hand and k=the # of kings in the hand, I am looking for pr{x=1 given k=1}, pr{x=2 given k=1}...pr{x=4 given k=1} – 2012-11-01
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0Since this is conditional, I know pr{x=1 given k=1} is equal to pr{x=1 and k=1}/pr{k=1} – 2012-11-01
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0and I know that pr{k=1}= [(4c1)(48c4)]/(52c5) – 2012-11-01
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1Intuitively it seems like it shouldn't matter at all... you've got *some* ranks in your hand, who cares if a king is one of them? Or do you mean that your hand contains *exactly* one king (not two or more)? – 2012-11-01
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0I mean exactly 1 king – 2012-11-02
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1@Elliot: That kind of clarification should be incorporated into the question so that people don't have to delve into the comments to understand the question unambiguously. – 2012-11-02
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0possible duplicate of [Conditional probability within a poker hand](http://math.stackexchange.com/questions/225695/conditional-probability-within-a-poker-hand) – 2012-11-02
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0I've edited your title to match the body, and rephrased the body. I you intended the body to match the title, please change the title back, and change "$1$ ace and $1$ queen" in the body to "$1$ king". – 2012-11-02