Yahtzee 4 of a Kind
In a yahtzee roll, calculate the probability of
4 of a Kind
4 of a Kind Probability Formula
Probability of 4 of a kind = Probability[4(1s or 2s or 3s or 4s or 5s or 6s & unequal 5th die)]
Probability of four = 1's
Probability of 4 1's = All possibilities of 4 1's & unequal 5th die * 6 die faces
P(1,1,1,1,not 1) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
| P(1,1,1,1,not 1) = | 5 |
| 7,776 |
Probability of four = 2's
Probability of 4 2's = All possibilities of 4 2's & unequal 5th die * 6 die faces
P(2,2,2,2,not 2) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
| P(2,2,2,2,not 2) = | 5 |
| 7,776 |
Probability of four = 3's
Probability of 4 3's = All possibilities of 4 3's & unequal 5th die * 6 die faces
P(3,3,3,3,not 3) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
| P(3,3,3,3,not 3) = | 5 |
| 7,776 |
Probability of four = 4's
Probability of 4 4's = All possibilities of 4 4's & unequal 5th die * 6 die faces
P(4,4,4,4,not 4) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
| P(4,4,4,4,not 4) = | 5 |
| 7,776 |
Probability of four = 5's
Probability of 4 5's = All possibilities of 4 5's & unequal 5th die * 6 die faces
P(5,5,5,5,not 5) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
| P(5,5,5,5,not 5) = | 5 |
| 7,776 |
Probability of four = 6's
Probability of 4 6's = All possibilities of 4 6's & unequal 5th die * 6 die faces
P(6,6,6,6,not 6) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
| P(6,6,6,6,not 6) = | 5 |
| 7,776 |
Probability of 4 of a kind
Probability of 4 of a kind = All possible of 4 of a kinds & unequal 5th die * 6 die faces
| Probability of 4 of a kind = | (5 + 5 + 5 + 5 + 5) x 6 die faces |
| 7,776 |
| Probability of 4 of a kinds = | 25 x 6 die faces |
| 7,776 |
| Probability of 4 of a Kind = | 150 |
| 7776 |
Final Answer
Using our GCF calculator, we reduce top and bottom by 6, to get
| Probability of 4 of a Kind = | 25 |
| 1,296 |
Probability of 4 of a Kind = 25/1,296
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What is the Answer?
Probability of 4 of a Kind = 25/1,296
How does the Yahtzee-1st Roll Calculator work?
Free Yahtzee-1st Roll Calculator - Calculates the probability of various scoring hands in the game of Yahtzee on the 1st roll of the dice.
This calculator has 1 input.
What 4 concepts are covered in the Yahtzee-1st Roll Calculator?
gamesprobabilitythe 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 OutcomesyahtzeeA dice game created by Milton Bradleyyahtzee-1st roll
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