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The probability of a hand containing one or more aces is equal to 1 minus the probability of the hand not containing any aces. The probability for each card will be 48/52 multiplied by 47/51 multiplied by 46/50 and so on. This gives 0.30382

1 minus this is 0.696

Therefore the probability of a 13-card hand containing one or more aces is 0.696

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Q: What is the probability of a 13-card hand containing one or more aces?
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In a poker hand consisting of 5 cards find the probability of holding 3 aces?

Approximately 2%


What is the probability of getting exactly three aces in a five-card poker hand dealt from an ordinary 52 card deck?

The probability of getting 3 aces in the order AAABB is; P(AAABB) = (4/52)∙(3/51)∙(2/50)∙(48/49)∙(47/48) = 0.0001736... There are 5C3 = 5!/(3!∙(5-3)!) = 10 different ways in which the aces can come out. So the probability of getting exactly three aces in a five card poker hand dealt from a 52 card deck is, P(3A) ~ 10∙(0.0001736) ~ 0.001736 ~ 0.1736%


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