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Suppose someone is continuously drawing one card each time (without replacement) from a deck of cards. He stops when he gets 3 of Hearts.

What's the probability that he gets any of the Aces before getting the 3 of Hearts?

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If you are asking about a specific Ace, it is clearly $\dfrac{1}{2}$.

If any Ace will do, just look at the order our $5$ cards come in. (The others are totally irrelevant.) The probability our $3$ comes first is $\dfrac{1}{5}$. So the probability it does not come first is $\dfrac{4}{5}$.

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    I had misread the question as $3$ is **first**.2012-10-04
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Assuming you mean all the aces are drawn before the 3 of hearts, the answer is $\frac{4}{5}$ because the 3 can come in any of 5 positions as marked in Xs below:

X A X A X A X A X 

Only the last position exhibits the condition in which all the aces have been drawn already.

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    I mean any of the aces will count.2012-10-04