Session 8, Part B:
Mathematical Probability

In This Part: Predicting Outcomes | Fair or Unfair? | Outcomes | Finding the Winner
Making a Probability Table

Recall the question from the last section. Each of the two players rolls a die, and the winner is determined by the sum of the faces:

 • Player A wins when the sum is 2, 3, 4, 10, 11, or 12. • Player B wins when the sum is 5, 6, 7, 8, or 9.

If this game is played many times, which player do you think will win more often, and why?

To analyze this problem effectively, we need a clear enumeration of all possible outcomes. Let's examine one scheme that is based on a familiar idea: an addition table.

Red Die

Blue Die

 + 1 2 3 4 5 6 1 2 3 4 5 6

Each possible outcome for the sum of the two dice can be enumerated in this table. For example, if the outcome were (1,1), here is how you would record it:

Red Die

Blue Die

 + 1 2 3 4 5 6 1 1 + 1 2 3 4 5 6

This is how you would record the outcome (2,4):

Red Die

Blue Die

 + 1 2 3 4 5 6 1 2 2 + 4 3 4 5 6

This is how you would record the outcome (4,2):

Red Die

Blue Die

 + 1 2 3 4 5 6 1 2 3 4 4 + 2 5 6

Note that the outcome (4,2) is different from the outcome (2,4).

Problem B4

 a. Complete this table of possible outcomes. (If you're doing it on paper, you do not have to use blue and red pencils, but be aware of the difference between such outcomes as 2 + 4 and 4 + 2.) b. How many entries will the table have? How does this compare to your answer to question (a)?

When you click "Show Answers," the filled-in table will appear below the problem. Scroll down the page to see it.

Red Die

Blue Die

 + 1 2 3 4 5 6 1 2 3 4 5 6

Red Die

Blue Die

 + 1 2 3 4 5 6 1 1 + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 2 2 + 1 2 + 2 2 + 3 2 + 4 2 + 5 2 + 6 3 3 + 1 3 + 2 3 + 3 3 + 4 3 + 5 3 + 6 4 4 + 1 4 + 2 4 + 3 4 + 4 4 + 5 4 + 6 5 5 + 1 5 + 2 5 + 3 5 + 4 5 + 5 5 + 6 6 6 + 1 6 + 2 6 + 3 6 + 4 6 + 5 6 + 6