Question

When rolling a 6-sided die twice, determine P(sum of 6).

twelve thirty sixths
seven thirty sixths
five thirty sixths

Answer 1

5/36

Explanation:

We can model the possible outcomes for rolling a 6-sided die twice in a table:

`\begin{array} c \underline{\text{roll 1}} & \underline{\text{roll 2}} & \underline{\text{sum}} \\1 & 1 & 2 \\1 & 2 & 3 \\1 & 3 & 4 \\1 & 4 & 5 \\1 & 5 & 6 \\1 & 6 & 7\end{array}`
`\begin{array} c\underline{\text{roll 1}} & \underline{\text{roll 2}} & \underline{\text{sum}} \\2 & 1 & 3 \\2 & 2 & 4 \\2 & 3 & 5 \\2 & 4 & 6 \\2 & 5 & 7 \\2 & 6 & 8\end{array}`

These are only a third of the possible outcomes. However, analyzing the sum columns, we can extrapolate the rest of the outcomes:

sum1 sum2 sum3 sum4 sum5 sum6

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

5 6 7 8 9 10

6 7 8 9 10 11

7 8 9 10 11 12

The number in "sum#" represents the second roll, and the row number (starting from 1 at the top) represents the first roll.

We can see that there are 5 possible outcomes where 6 is the sum of the rolled numbers, so P(sum of 6) = 5/36.