Question

If two standard number cubes are rolled 100 times, how would you predict the number of times that a sum of 7 or 11 will be rolled?

Answer 1

Roughly 22 times

Explanation:

We can calculate the odds, on any given role, the chance that a 7 or 11 will come up.

Let's say that one cube is Red and the other Green. We can get a 7 when we get:

`Rcolor(white)(000)G`

`1color(white)(0000)6`
`2color(white)(0000)5`
`3color(white)(0000)4`
`4color(white)(0000)3`
`5color(white)(0000)2`
`6color(white)(0000)1`

and so 6 ways to get a 7.

We can get an 11 when we get:

`5color(white)(0000)6`
`6color(white)(0000)5`

and so 2 ways.

We have 8 possible ways to get a 7 or 11.

On any given role, there are `6xx6=36` possible roles. And so on any given role, the odds of getting a 7 or 11 is:

`8/36`

To figure out the number of 7 or 11 in 100 roles, we can use a ratio:

`8/36=x/100`

and now let's solve for `x`:

`36x=800`

`x=800/36=22 2/9= 22.bar2` or roughly 22.