# Thread: trinomal distribution dice problem

1. ## trinomal distribution dice problem

Three fair dice are rolled simultaneously. In 10 independent throws,

let $\displaystyle X$: number of times all the dice show same face

let $\displaystyle Y$: number of times exactly $\displaystyle 2$ dice show same face

let p_1,p_2,p_3 be corresponding probabilities of
X, Y, Z=n-X-Y

pdf of trinomial distribution,

p(X=3, Y=3)= 10C3* (10-3)C3* p_1^3* p_2^3* p_3^4
i understand p_1= 6/6^3

but what are the values of p_2,p_3 ?

2. Originally Posted by amul28
Three fair dice are rolled simultaneously. In 10 independent throws,

let $\displaystyle X$: number of times all the dice show same face

let $\displaystyle Y$: number of times exactly $\displaystyle 2$ dice show same face

let p_1,p_2,p_3 be corresponding probabilities of
X, Y, Z=n-X-Y

pdf of trinomial distribution,

p(X=3, Y=3)= 10C3* (10-3)C3* p_1^3* p_2^3* p_3^4
i understand p_1= 6/6^3

but what are the values of p_2,p_3 ?
How many ways can exactly two dice show the same face? Divide that number by 6^3.

p3 = 1 - (p1 + p2).