Question

A pair of fair dice is tossed and the up face values are observed. Define X to be the number of ones observed. Find P(X = 0).

Answer 1

solution:

When a pair of fair dice is tossed and up face values are observed.

we have sample space

S = { (1,1) ,(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1) ,(2,2),(2,3),(2,4),(2,5),(2,6)

    (3,1) ,(3,2),(3,3),(3,4),(3,5),(3,6)

   (4,1) ,(4,2),(4,3),(4,4),(4,5),(4,6)

    (5,1) ,(5,2),(5,3),(5,4),(5,5),(5,6)

    (6,1) ,(6,2),(6,3),(6,4),(6,5),(6,6) }

n(S) = 36

Let X be the discrete random variable representing no.of ones observed

Then possible values of X = X(S) = { 0,1,2 }

Here, n(X=0) = 25 = { (2,2),(2,3),(2,4),(2,5),(2,6)

(3,2),(3,3),(3,4),(3,5),(3,6)

(4,2),(4,3),(4,4),(4,5),(4,6)

(5,2),(5,3),(5,4),(5,5),(5,6)

(6,2),(6,3),(6,4),(6,5),(6,6) }

Therefore , P(X=0) = n(X=0) / n(S) = 25/36

[ ~ we get P(X=1) = 10/36 , P(X=2) = 1/36 ]