auto23652im

2022-07-01

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

Franco Cohen

Expert

Step 1
If you toss the die twice, there are $6×6=36$ 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 $2\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to$ this can only come from $1+1=2$
a total of $3\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to$ this can come from $1+2=3\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}2+1=3$
a total of $12\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to$ this can only come from $6+6=12$
Step 2
So, of the total of 36 possible outcomes, there are only 4 that we want.
$P\left(2,3,12\right)=\frac{4}{36}=\frac{1}{9}$

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