# If you roll two dice, what is the probability of rolling a 3 and an even number?

Oct 31, 2015

$\frac{1}{6}$

#### Explanation:

The probability of rolling a 3 is $\frac{1}{6}$.
The probability of rolling an even number is $\frac{3}{6}$.
Therefore by the multiplication principle, the probability of both the one and the other event occurring is $\frac{1}{6} \times \frac{3}{6} = \frac{1}{12}$

This is when you first roll a 3 and then an even number.
The probability of first rolling an even number and then a 3 is exactly the same.

So the probability of rolling a 3 and an even number (in whatever order) are (adding the chances now):
$\frac{1}{12} + \frac{1}{12} = \frac{1}{6}$