Question

When two dice are rolled what is the probability of getting a sum less than 6 ?

Answer 1

`5/18`

Explanation:

The easiest method is to draw a possibility space first.
The grid shows the totals for two dice.

`6|" "7" "8" "9" "10" "11" "12`
`5|" "6" "7" "8" "9" "10" "11`
`4|" "color(blue)(5)" "6" "7" "8" "9" "10`
`3|" "color(blue)(4" "5)" "6" "7" "8" "9`
`2|" "color(blue)(3" "4" "5)" "6" "7" "8`
`1|ul(" "color(blue)(2" "3" "4" "5)" "6" "7)`
`color(white)(xxxx)1" "2" "3" "4" "5" "6`

There are: `6xx6 = 36` possible outcomes.
Of these there are `color(blue)(10)` totals which are less than `6`.

`:.P("less than 6") = 10/36 = 5/18`