Probability of getting 4 aces out of a hand of 5

In summary, the probability of getting 4 aces out of a hand of 5 is 0.000181 or approximately 0.0181%. This can be calculated by determining the total number of combinations of 5 cards from a standard deck of 52 cards and then dividing the number of combinations with 4 aces by the total number of combinations. The probability of getting 4 aces and a king out of a hand of 5 is even lower at 0.00000000000545 or approximately 0.000000000545%. This probability will not change as long as the deck of cards is standard and the method of drawing is random, but it can be increased by using a deck with more aces
  • #1
Unite1133
1
0
If you have a standard deck of 52 cards, what is the probability that out of a hand of 5 cards you get 4 aces?



First I found the total # of ways for choosing 5 cards from 52 = (52 C 5) = 2,598,960
Then the # of hands which has 4 aces is 48 (because the 5th card can be any of 48 other cards).
So there is 1 chance in (2,598,960/48) = 54,145 of being dealt 4 aces in a 5 card hand.
The probability is 1/54,145 ≈ .0018469%

Did I do this right?
 
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  • #2
Looks ok to me.
 

1. What is the probability of getting 4 aces out of a hand of 5?

The probability of getting 4 aces out of a hand of 5 is 0.000181 or approximately 0.0181%. This means that out of all possible combinations of 5 cards, there is only a 0.0181% chance of getting 4 aces.

2. How do you calculate the probability of getting 4 aces out of a hand of 5?

To calculate the probability, you need to first determine the total number of possible combinations of 5 cards from a standard deck of 52 cards. This is calculated using the combination formula nCr = n! / (r!(n-r)!), where n is the total number of cards (52) and r is the number of cards in the hand (5). Then, you need to determine the number of combinations that contain 4 aces, which is 4C4 = 1. Finally, divide the number of combinations with 4 aces by the total number of combinations to get the probability.

3. What is the probability of getting 4 aces and a king out of a hand of 5?

The probability of getting 4 aces and a king out of a hand of 5 is 0.00000000000545 or approximately 0.000000000545%. This is an incredibly rare event, as it requires getting all 4 aces and one specific king out of a total of 52 cards.

4. Can the probability of getting 4 aces out of a hand of 5 change?

No, the probability of getting 4 aces out of a hand of 5 will not change as long as the deck of cards is standard and the method of drawing the cards is random. This probability is based on the total number of cards in a deck and the specific number of aces in the deck, which will not change.

5. Is it possible to increase the probability of getting 4 aces out of a hand of 5?

Yes, the probability of getting 4 aces out of a hand of 5 can be increased by using a deck with more aces (e.g. a deck with 6 aces instead of 4) or by increasing the number of cards in the hand (e.g. a hand of 6 cards instead of 5). However, this also increases the total number of possible combinations and therefore, the overall probability will still be very low.

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