# You roll 2 dice. What is the probability that the sum of the die is even and one shows a 3?

Jan 31, 2017

$= \frac{5}{36}$

#### Explanation:

we also can write as
$\left(1 , 1\right) , \ldots \left(1 , 6\right)$,
$\left(2 , 1\right) , \ldots \left(2 , 6\right)$,
(3,1),...((3,6),
$\left(4 , 1\right) , \ldots \left(4 , 6\right)$,
$\left(5 , 1\right) , \ldots \left(5 , 6\right)$, and
$\left(6 , 1\right) , \ldots \left(6 , 6\right)$

and it total is $36$.
therefore $n \left(\xi\right) = 36$

Let say that $A$ is an outcome for which a 3 must one show and their sum is even are (3,1),(3,3),(3,5), (1,3) and(5,3), therefore $n \left(A\right) = 5$

Probability A =$\frac{n \left(A\right)}{n \left(\xi\right)}$

$= \frac{5}{36}$

Jan 31, 2017

$p = \frac{5}{36}$

#### Explanation:

There are 36 outcomes. Of which 5 are favourable.

Probability = Number of favourable outcomes)/ Total number of outcomes

$p = \frac{5}{36}$