Answer
Success!
Decimal probability = 0.000240096
↓Steps Explained:↓
In a standard 5-card poker hand for 1 deck:
Calculate P(4 of a kind)
4 of a kind Hands
Calculate Total 5 Card hands
| Total Hands = | 52! |
| (52-5)! * 5! |
| Total Hands = | 52! |
| 47! * 5! |
| Total Hands = | (52 * 51 * 50 * 49 * 48) * 47! |
| 47! * (5 * 4 * 3 * 2 * 1) |
Cancelling the 47!, we get:
| Total Hands = | 311,875,200 |
| 120 |
Total Hands = 2,598,960
Build Probability
Possible 4 of a kinds = Possible ways to get 4 cards of one kind and any 5th card
Possible 4 of a kinds = 13 different 4 of a kind choices * 48 remaining 5th cards = 624
| Probability of a 4 of a kind = | Possible 4 of a kind hands |
| Total Hands |
Reduce top and bottom by 624
GCF = Greatest Common Factor
| P(4 of a kind) = | 624 |
| 2,598,960 |
GCF for 1 and 4165 = 624
| P(4 of a kind) = | 1 |
| 4,165 |
Final Answer
Decimal probability = 0.000240096Take the Quiz
Related Calculators: Hypergeometric Distribution | Hardy-Weinberg | Fishers Exact Test