# For the experiment of tossing a six sided die twice, what is the probability that the sum is 2, 3 or 12?

Mar 13, 2018

$P \left(2 , 3 , 12\right) = \frac{4}{36} = \frac{1}{9}$

#### Explanation:

If you toss the die twice, there are $6 \times 6 = 36$ different outcomes.
Each of the $6$ numbers for the first throw can be combined with each of the same six for the second throw.

Of those $36$ outcomes, we only want:

a total of $2 \text{ } \rightarrow$ this can only come from $1 + 1 = 2$
a total of $3 \text{ } \rightarrow$ this can come from $1 + 2 = 3 \mathmr{and} 2 + 1 = 3$
a total of $12 \text{ } \rightarrow$ this can only come from $6 + 6 = 12$

So, of the total of $36$ possible outcomes, there are only $4$ that we want.

$P \left(2 , 3 , 12\right) = \frac{4}{36} = \frac{1}{9}$