Question

Find the probability of rolling a sum less than 6 or a sum greater than 8 when a pair of dice is rolled?

Answer 1

`(5)/(9)\approx0.556`

Explanation:

A pair of dice is rolled so the outcome space will be.

`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)\}`

Total number of elements
`=36`

Possible outcomes in which sum is less than
`6` or greater than
`8`

`S_(1) = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(3,6),\\(4,1),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}`

Number of element in this space
`=20`

P(sum is less than
`6` or greater than
`8`)

`=(Favourable\ outcomes)/(total\ outcomes) \\=(20)/(36)\\ =(5)/(9)`