# Two fair dice are thrown,what is the probability of getting two odd numbers?

Jun 28, 2018

$\frac{1}{4}$

#### Explanation:

The two dice are independent, i.e. the result of one die does not infuence the result of the other.

In this case, the probability of a complex event is the product of the probabilities of the simple events.

For every die, there are $3$ odd outcomes and $3$ even outcomes. So, the probability of getting an odd number is $\frac{3}{6} = \frac{1}{2}$

So, the probability that this happens with both dice is $\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$

In this case, it is actually easy to enumerate the "good" outcomes: there are $36$ outcomes in total (all numbers from $1$ to $6$ for one die and the same for the other die). The good outcomes are

$\left(1 , 1\right)$, $\left(1 , 3\right)$, $\left(1 , 5\right)$

$\left(3 , 1\right)$, $\left(3 , 3\right)$, $\left(3 , 5\right)$

$\left(5 , 1\right)$, $\left(5 , 3\right)$, $\left(5 , 5\right)$

And in fact, $9$ good outcomes over $36$ total outcomes means

$\frac{9}{36} = \frac{1}{4}$