In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 1 on at least one of the number cubes. Make a list of all the different possible outcomes when two number cubes are rolled. (2 points for listing all of the possible outcomes) What fraction of the possible outcomes is favorable? (1 point for the correct numerator/1 point for the correct denominator) Suppose you rolled the two number cubes 100 times, would you expect at least one 1 more or less than 34 times? Explain. (1 point for your explanation)

Accepted Solution

There are 11 possible outcomes that contain a 1.
1-1  1-2  1-3  1-4  1-5  1-6  
2-1  3-1  4-1  5-1  6-1

That makes a fraction of 11 out of 36.

If you rolled the cubes 100 times, you should expect to get:
(11/36) x 100 = 30.555 about 31 times.
That is less than 34 times.