Yahtzee 4 of a Kind

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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

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

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

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

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

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

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

Final Answer

Using our GCF calculator, we reduce top and bottom by 6, to get