Question

When a pair of dice is rolled (one is yellow and the other is green), then

• A. total number of elements in sample space is $6\times 6$
• B. sample space is $\{(1,1),(1,2),(1,3),(1,4)$,
  $(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$,
  $(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\}$
• C. both (a) and (b)
• D. total number of elements in sample space is $6+6$

Answer 1

Answer: (A)

The sample space is given by $S=\{(x,y):x$ is the number on the yellow die and $y$ is the number on the green die$\}$. The number of elements of this sample space is $6\times 6=36$ and the sample space is given below :
$\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2)$,
$(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4)$,
$(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$,
$(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2)$,
$(6,3),(6,4),(6,5),(6,6)\}$.