Answer:
The probability that exactly one card is an ace when three cards are dealt from a standard poker deck without replacement is 0.00018, or about 0.018%.
Explanation:
To find the probability that exactly one card is an ace when three cards are dealt from a standard poker deck without replacement, we need to consider the number of favorable outcomes (number of ways to choose one ace from the four available) and the number of total outcomes (number of ways to choose any three cards from the deck).
Number of favorable outcomes:
There are four aces in a standard poker deck, and we need to choose exactly one of them. So, the number of favorable outcomes is 4C1 = 4.
Number of total outcomes:
We need to choose any three cards from the deck, which can be done in 52C3 ways. The total number of outcomes is 52C3.
Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the number of total outcomes.
Probability = (Number of favorable outcomes) / (Number of total outcomes)
Probability = 4C1 / 52C3
To calculate this probability, we can use the formula for combinations:
4C1 = 4! / (1! * (4-1)!) = 4
52C3 = 52! / (3! * (52-3)!) = 22,100
Probability = 4 / 22,100 ≈ 0.00018
Therefore,
The probability that exactly one card is an ace 0.018%.