# How do you determine the sample space for the experiment where a six sided die is tossed twice and the sum of the points is recorded?

Nov 14, 2017

Show an array of the $36$ possible outcomes.

#### Explanation:

A sample space or possibility space is similar to a graph.

The first throw is shown on one axis and the second throw is shown on the other axis. There are 6 possible outcomes each time:
The sum of the two throws is shown on the grid.

second throw
$\downarrow$

$6 : \text{ "7" "8" "9" "10" "11" } 12$

$5 : \text{ "6" "7" "8" "9" "10" } 11$

$4 : \text{ "5" "6" "7" "8" "9" } 10$

$3 : \text{ "4" "5" "6" "7" "8" } 9$

$2 : \text{ "3" "4" "5" "6" "7" } 8$

$1 : \text{ "2" "3" "4" "5" "6" } 7$
$\uparrow$
$\text{ "rarr1" "2" "3" "4" "5" "6" } \leftarrow$ first throw

There are $6 \times 6 = 36$ possible outcomes.

The highest total is $6 + 6 = 12$
The lowest total is $1 + 1 = 2$