Probability of 2 pair

Probability of 2 pair

In a standard 5-card poker hand for 1 deck:

Calculate P(2 pair)

2 pair Hands

Calculate Total 5 Card hands

Choose 5 cards from 52 cards

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 = 0.0475390156

You have 1 free calculations remaining

What is the Answer?

Decimal probability = 0.0475390156

How does the 5 Card Poker Hand Calculator work?

Free 5 Card Poker Hand Calculator - Calculates and details probabilities of the 10 different types of poker hands given 1 player and 1 deck of cards.
This calculator has 1 input.

What 1 formula is used for the 5 Card Poker Hand Calculator?

Total Possible 5 Card Hands = 2,598,960

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the 5 Card Poker Hand Calculator?

5 card poker handcombinationa mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)!factorialThe product of an integer and all the integers below itprobabilitythe likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes

Example calculations for the 5 Card Poker Hand Calculator

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