Question

When rolling two standard six-sided dice, what is the probability that the sum of the dice will be even or a multiple of 3? (show your work)

Answer 1

2/3

Explanation:

List all the possible sums. If it helps, make a table:

`\left[\begin{array}{ccccccc} &1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right]`

There are 36 total possible sums. Of those, 18 are even, and 6 are odd but multiples of 3.

Therefore, the probability is:

P = (18 + 6) / 36

P = 24 / 36

P = 2 / 3