In a yahtzee roll, calculate the probability of
Full House
Full House Probability Formula
Probability of a Full House = Probability of 3 of a kind and 1 pair
Total Combos
Probability of a Full House = Total Combos of 3 of a kind and 1 pair/All Possible Rolls
Total Combos of 3 of a kind and 1 pair = Combos of 3 of a kind with 3 (1's) and any 1 pair * 6 die faces
Total Combos of 3 of a kind and 1 pair = 1 pair in roll (4,5)(3,5)(2,5)(1,5)(3,4)(2,4)(1,4)(2,3)(1,3)(1,2)
Total Combos of 3 (1's) and 1 pair * 10 = (1-1-1-2-2) + (1-1-1-3-3) + (1-1-1-4-4) + (1-1-1-5-5) + (1-1-1-6-6) * 10
Total Combos of 3 (1's) and 1 pair * 10 = 5 * 10
Total Combos of 3 (1's) and 1 pair * 10 = 50
3 of a kind with pair combos
Combos of 3 of a kind with 3 (1's) and 1 pair * 6 die faces = 50 * 6
Total Combos of 3 of a kind and 1 pair = 300
Total Possible Die Roll Combos = 6 * 6 * 6 * 6 * 6
Total Possible Die Roll Combos = 7,776
Plug in numbers
| Probability of a Full House = | Total Full House Combos |
| Total Possible Die Roll Combos |
| Probability of a Full House = | 300 |
| 7776 |
Final Answer
Using our GCF calculator, we reduce top and bottom by 12, to get
| Probability of a Full House = | 25 |
| 648 |
What is the Answer?
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What 4 concepts are covered in the Yahtzee-1st Roll Calculator?
- games
- probability
- the 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 - yahtzee
- A dice game created by Milton Bradley
- yahtzee-1st roll
