Question

What's the probability of rolling a 9 or higher using two fair standard dice?

Answer 1

`10/36=5/18=27.bar7%`

Explanation:

The rolls you can get with 2 six-sided dice is in this table:

`((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))`

See that there are 10 numbers that are 9 or higher out of a total number of 36 possibilities, giving a probability of `10/36=5/18=27.bar7%`

Answer 2

total no. of outcomes`= 6×6`
favourable outcomes require that sum should be `>=9` .
favourable outcomes are
for `9 (4,5),(5,4),(6,3),(3,6)`
for `10 (5,5),(6,4),(4,6)`
for `11 (5,6),(6,5)`
for `12 (6,6)`;
probability `=10/36=5/18~~27.7777777778%`