Jovany Clayton

2022-07-07

For the experiment of tossing a six sided die twice, what is the probability that the sum is less than 11?

Dalton Lester

Expert

Step 1
Without loss of generality we could assume that one die is $\text{red}$ and the other is $\text{green}$
For each of the 6 $\text{red}$ outcomes there are 6 $\text{green}$ outcomes.
This means that there are a combined collection of $6×6=36$ possible outcomes.
Step 2
Of the 36 possible outcomes only 3 result in totals greater than on equal to 11; namely $\text{XXX}<\text{red},\text{green}>\in \left\{<5,6>,<6,5>,<6,6>\right\}$
Therefore, there are $36-3=33$ possible outcomes for which the sum is less than 11.
Since each outcome is (assumed to be) equally probable, $\text{XXX}P\left(\text{sum}<11\right)=\frac{33}{36}=\frac{11}{12}$

Do you have a similar question?