1. in a board game, you must roll two 6-sided number cubes. you can only start the game if you roll a 3 on at least one of the number cubes.

(a) make a list of all the different possible outcomes when two number cubes are rolled

(b) what fraction of the possible outcomes is favorable?

(c) suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? explain.

The list
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6

The favorable combinations are any with a 3 in them
There are a total of 11 with 3
so there are 11 favorable combinations
The fraction is 11/36

To find how many out of 100 do
100/36= 2.777...which rounds to 3
3×11=33
If you rolled the dice 100 times you would expect at least one 3 more or less than 34 times