# In a game two fair number cubes are rolled. To make the first move, you need to roll a total of 6, 7, or 8. What is the probability that you will be able to make the first move?

16/36=4/9~=44.4%

#### Explanation:

For anyone who saw the short gibberish before I got to the edit button - that was my cat answering (he actually posted the whole thing before I got to it).

Ok - on to the question:

Let's first see the possible die results:

$\left(\begin{matrix}\textcolor{w h i t e}{0} & \underline{1} & \underline{2} & \underline{3} & \underline{4} & \underline{5} & \underline{6} \\ 1 | & 2 & 3 & 4 & 5 & 6 & 7 \\ 2 | & 3 & 4 & 5 & 6 & 7 & 8 \\ 3 | & 4 & 5 & 6 & 7 & 8 & 9 \\ 4 | & 5 & 6 & 7 & 8 & 9 & 10 \\ 5 | & 6 & 7 & 8 & 9 & 10 & 11 \\ 6 | & 7 & 8 & 9 & 10 & 11 & 12\end{matrix}\right)$

There are 5 ways to roll a six, 6 ways to roll a seven, and 5 ways to roll an eight. That's 16 rolls that will allow for a first move.

There are 36 possible rolls.

This means that there is a 16/36=4/9~=44.4% of being able to make a first move.