Question

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?

Answer 1

`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:

`((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(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))`

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.