Answer to Question #287834 in Statistics and Probability for sid

Question

  Two dice are rolled. Let B be the random variable representing the number of

            outcomes with 6 turn up. Find the values of the random variable B.

 

Answer 1

The outcomes of rolling two dice is given as,

$S=\begin{Bmatrix} (1,1) & (2,1)&(3,1)&(4,1)&(5,1)&(6,1) \\ (1,2) & (2,2)&(3,2)&(4,2)&(5,2)&(6,2)\\ (1,3)&(2,3)&(3,3)&(4,3)&(5,3)&(6,3)\\ (1,4)&(2,4)&(3,4)&(4,4)&(5,4)&(6,4)\\ (1,5)&(2,5)&(3,5)&(4,5)&(5,5)&(6,5)\\ (1,6)&(2,6)&(3,6)&(4,6)&(5,6)&(6,6) \end{Bmatrix}$

$B$ is a random variable representing the number of outcomes with 6.

From the sample space above, the outcomes with 6 are, 1,2,3,4,5,6.

Therefore, the random variable $B$ may take on the following values.

$b=1,2,3,4,5,6$

When a 6 turn up, the number of outcomes are 11.