Data Session 8, Part B: Mathematical Probability

Session 8, Part B:
Mathematical Probability

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

Another way to solve this problem is to look at a probability table for the sum of the two dice. This representation can be quite useful, since it gives us a complete description of the probabilities for the different values of the sum of two dice, independent of the rules of the game. Note 6

Again, here are the sums of the possible outcomes for the two dice:

Red Die

Blue Die

+

1

2

3

4

5

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

•	Only one of the outcomes (highlighted in purple) produces a sum of 2. There are 36 equally likely outcomes. So the probability of the sum being 2 is 1/36.
•	Two of the outcomes (highlighted in green) produce a sum of 3. There are 36 equally likely outcomes. So the probability of the sum being 3 is 2/36.

Here is the start of a probability table for the sum of two dice:

Problem B7

Complete the probability table.

Sum

Frequency

Probability

2

1

1/36

3

2

2/36

4

5

6

7

8

9

10

11

12

Sum

Frequency

Probability

2

1

1/36

3

2

2/36

4

3

3/36

5

4

4/36

6

5

5/36

7

6

6/36

8

5

5/36

9

4

4/36

10

3

3/36

11

2

2/36

12

1

1/36

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Problem B8
Use the probability table you completed in Problem B8 to determine the probability that Player A will win the game. Recall that Player A wins if the sum is 2, 3, 4, 10, 11, or 12.


Problem B9
If you know the probability that Player A wins, how could you use it to determine the probability that Player B wins without adding the remaining values in the table?

If Player A does not win, then Player B wins. Close Tip

Next > Part C: Analyzing Binomial Probabilities

Session 8: Index | Notes | Solutions | Video