Question

What's the probability of rolling less than or equal to 7 on two fair regular number cubes?

Answer 1

`P("sum of 2 number cubes" <=7)=21/36=7/12`

Explanation:

I'm going to assume we're working with 2 fair, standard, 6-sided dice.

Let's take a look at all possible rolls:

`((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))`

Out of the 36 total possible combinations, 15 are greater than seven (which means that `36-15=21` are equal to or less than seven). We can express this a couple of ways:

• `P("sum of 2 number cubes" <=7)=21/36=7/12`

• `P("sum of 2 number cubes" <=7)=1-P("sum of 2 number cubes" >7)=1-15/36=21/36=7/12`