Suppose you roll two dice. How do you find the probability that you'll roll a sum of 7?

Dec 31, 2016

Probability that you'll roll a sum of $7$ is $\frac{1}{6}$

Explanation:

When we roll a dice, we can get numbers $1$ to $6$ on each of the dices and hence possible combinations are as follows (here $\left(x , y\right)$ means we get $x$ on first dice and $y$ on second dice.)

$\left(1 , 1\right)$, $\left(1 , 2\right)$, $\left(1 , 3\right)$, $\left(1 , 4\right)$, $\left(1 , 5\right)$, $\left(1 , 6\right)$,

$\left(2 , 1\right)$, $\left(2 , 2\right)$, $\left(2 , 3\right)$, $\left(2 , 4\right)$, $\left(2 , 5\right)$, $\left(2 , 6\right)$,
.
.
.
$\left(6 , 1\right)$, $\left(6 , 2\right)$, $\left(6 , 3\right)$, $\left(6 , 4\right)$, $\left(6 , 5\right)$, $\left(6 , 6\right)$.

total $36$ possibilities,

of which only $\left(1 , 6\right)$, $\left(2 , 5\right)$, $\left(3 , 4\right)$, $\left(4 , 3\right)$, $\left(5 , 2\right)$ and $\left(6 , 1\right)$

i.e. $7$ possibilities, result in a sum of $7$.

Hence, probability that you'll roll a sum of $7$ is $\frac{6}{36} = \frac{1}{6}$