Answer
Success!
Decimal probability = 0.0475390156
↓Steps Explained:↓
In a standard 5-card poker hand for 1 deck:
Calculate P(2 pair)
2 pair 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 2 pairs = 13 cards to choose from in combinations of 2
Possible ways to choose ranking of 2 pairs = 13!/(2! * 11!)
Possible ways to choose ranking of 2 pairs = (13 * 12)/2 = 78
Possible ways to choose 2 combos of 4 cards = [4!/(2! * 2!)]2 = [(4 * 3)/2]2 = 36
36 Possible choices * 78 2 pair combos * 44 5th cards = 2,808 * 44 5th cards
Possible 3 of a kinds = 123552
| Probability of 2 pair = | Possible 2 pair hands |
| Total Hands |
Reduce top and bottom by 624
GCF = Greatest Common Factor
| P(2 pair) = | 123,552 |
| 2,598,960 |
GCF for 198 and 4165 = 624
| P(2 pair) = | 198 |
| 4,165 |
Final Answer
Decimal probability = 0.0475390156Take the Quiz
Related Calculators: Hypergeometric Distribution | Hardy-Weinberg | Fishers Exact Test