Question fd3c6

Jun 2, 2017

33%, or 50%, depending.

Explanation:

There are two possible outcomes here, one where we only use unique outcomes (if we roll 6-4 we cannot use 4-6), and one where we use all outcomes.

For both, the amount of rolls available are 36. Of these, half are divisible by 2, so 18.
For non-unique rolls, 18 is the answer, and 18/36 = 1/2 = 50%, one of the answers.
For unique rolls, it is slightly different. Where before the ways to get an even number were numerous, from 6-6 to 1-1, we now have to get rid of duplicates. This includes 6-4/4-6, 5-3/3-5, 6-2/2-6, 4-2/2-4, 5-1/1-5 and 3-1/1-3. This gets rid of 6 possibilities, $18 - 6 = 12$ and 12/36 = 1/3 = 33%#.

Jun 2, 2017

$\frac{2}{9}$

Explanation:

Number of outcome $= 36$

Set of outcome with diffrence of 2$= \left\{\begin{matrix}1 & 3 \\ 2 & 4 \\ 3 & 1 \\ 3 & 5 \\ 4 & 2 \\ 4 & 6 \\ 5 & 3 \\ 6 & 4\end{matrix}\right\}$

Number of outcome with difference of $2 = 8$

Therefore,
the probability of outcome with difference of 2 $= \frac{8}{36} = \frac{2}{9}$