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Learning Math Home
Data Session 8, Part B: Mathematical Probability
 
Session 8 Part A Part B Part C Part D Homework
 
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Session 8 Materials:
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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:

Sum

Frequency

Probability

2

1

1/36

3

2

2/36


 

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

show answers

 

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

hide answers


 

Problem B8

Solution  

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

Solution  

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?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
If Player A does not win, then Player B wins.   Close Tip

Next > Part C: Analyzing Binomial Probabilities

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