# 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?

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:

$R \textcolor{w h i t e}{000} G$

$1 \textcolor{w h i t e}{0000} 6$
$2 \textcolor{w h i t e}{0000} 5$
$3 \textcolor{w h i t e}{0000} 4$
$4 \textcolor{w h i t e}{0000} 3$
$5 \textcolor{w h i t e}{0000} 2$
$6 \textcolor{w h i t e}{0000} 1$

and so 6 ways to get a 7.

We can get an 11 when we get:

$5 \textcolor{w h i t e}{0000} 6$
$6 \textcolor{w h i t e}{0000} 5$

and so 2 ways.

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

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

$\frac{8}{36}$

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

$\frac{8}{36} = \frac{x}{100}$

and now let's solve for $x$:

$36 x = 800$

$x = \frac{800}{36} = 22 \frac{2}{9} = 22. \overline{2}$ or roughly 22.