# How many outcomes will constitute the sample space resulting from rolling a pair of balanced 6-sided dice?

Feb 28, 2015

The sample space is $6 \cdot 6 = 36$

The first die has $6$ possible outcomes, as does the second.

Since these events are independent from each other, you must multiply the possibilities of the two events.

Or:
You can write out all possibilities, from $11 , 12 , 13$... all the way up to ...$65$ and $66$
Remember that $14$ is NOT the same as $41$, and you will also find $36$ possibilities.

Extra :
Example: if you want to calculate the probability of rolling a total of $5$, this can be done in the following ways:
$14 , 23 , 32 , 41 \to 4$ ways.

Probability is then "favourable"/"total"=4/36=1/9~~11%