# Kevin is rolling two dice together and adding them up. Which sums should come up the most frequently?

Feb 15, 2018

$7$

#### Explanation:

sample space: all possible outcomes of an experiment

here is the sample space of rolling two dice:

with a fair dice, all numbers are equally as likely to be rolled.

this means that the sum(s) most likely to come up are those that occur most frequently in the sample space.

the number of possible outcomes in terms of sums is $36$.

here are the sums and the number of times that they occur in the sample space:

$2 : 1$
$3 : 2$
$4 : 3$
$5 : 4$
$6 : 5$
$7 : 6$
$8 : 5$
$9 : 4$
$10 : 3$
$11 : 2$
$12 : 1$

$7$ occurs most frequently in the sample space, as the sum of $1 + 6$, $6 + 1$, $5 + 2$, $2 + 5$, $3 + 4$ and $4 + 3$.

since all numbers $1 - 6$ on the dice are equally likely to come up, $7$ is the most likely sum.