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?

Question

3918 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-25T03:57:06

Roughly 22 times

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.