Question

What is the probability of rolling, using 2 fair number cubes, either a roll that sums to less than 10 or is a doubles?

Answer 1

`28/36=7/9`

Explanation:

The possible rolls of a pair of fair dice is:

`((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(1|,2,3,4,5,6,7),(2|,3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,12))`

The number of rolls that are 10 and above is 6, which means the number of rolls that sum to less than 10 is `36-10=26`. To this, we need to add double 5 (sum 10) and double 6 (sum 12), for a total of 28 rolls that meet the conditions. This is from a possible 36 rolls, giving a probability of:

`28/36=7/9`