Activity: Investigating Two Dice

 

The purpose of this problem is to find the range of possible outcomes for rolling two dice just in case you go to Atlantic City or Las Vegas.  Remember, an important part of this exercise is writing all the possible outcomes and your reasons for the outcome that you think is most probable.

 

Step 1

Use the table below to record the results of rolling both dice. Follow the directions carefully. Roll the dice 36 times, carefully recording your results. When done, answer the following questions about your results.

 

Activity Reporting Form

 

As you roll your dice record the results on the form below. An outcome is the sum of the two dice. Place a checkmark in the ÒonceÓ column beside that outcome. For example if a 2 and a 3 appear on the dice then you would put a check mark in the 5 outcome row under ÒonceÓ. When an outcome occurs a second time then place a checkmark in the ÒtwiceÓ column, a third time would have us putting a check mark in the Ò3xÓ or Ò3 timesÓ column. You will be done when 36 check marks are on your grid.

 

                                    Make your tally checks or marks in the boxes

 Outcome       once   twice    3x      4x      5x       6x      7x      8x       9x      10x

1

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

         4

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

 

 

 

8

 

 

 

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

 

 

 

       10

 

 

 

 

 

 

 

 

 

 

       11

 

 

 

 

 

 

 

 

 

 

       12

 

 

 

 

 

 

 

 

 

 

       13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 2 Answer Questions:

What was the most frequent outcome?

 

 

 

 

 

 

What was the least frequent outcome?

 

 

 

 

 

 

How often did you roll an outcome of 1?

 

 

 

 

 

 

What do you think the likelihood is of rolling a 1?

 

 

 

 

 

 

How often did you roll an outcome of 12?

 

 

 

 

 

 

What do you think has the greater likelihood, rolling a 7 or rolling a 12? Why?

 

 

 

 

 

 

 

 

 

 

 

 


Determine the Sample Space (possible outcomes) for Our Dicey Problem

 

Part 2: What is the sample space for this experiment?

A sample space lists all of the outcomes that will occur from performing the experiment. In this case it would list all the possible outcomes of rolling two dice. On the grid below identify all the possible ordered pairs for the two dice and write their sum in the box.

 

 

 

Face of die 1 (Green die)

 
 

 

 

 

 

 

 

 

 

 

 



Continuing the Dicey Problem – What is the Probability?

 

Now that you have determined the sample space, the following outcomes can be determined by counting the number of favorable events in the sample space.

 

 

                                                                                            Number of           Probability

                                    Favorable Outcome                            Ways               of Occurring

The outcome shows a sum of 2

 

 

 

 

The outcome shows a sum of 7

 

 

 

 

The outcome shows a sum which is an even number

 

 

 

The outcome shows a sum of 6

 

 

 

 

The outcome shows a sum of 1

 

 

 

 

The outcome on each die is the same number (doubles)

 

 

 

The outcome shows Òsnake eyesÓ (double ones)

 

 

 

The outcome shows a sum of 13

 

 

 

 

 

 

Which outcome has the highest probability of occurring?

 

Which outcome has the least probability of occurring?

 


Food for Thought: Part 3

 

Suppose you decide to repeat this experiment again, but together with other classmates you decide to roll the dice 360 times. Can you give an estimate for how many times each of the following events will tally out of 360 tries?

 

 

The dice show a sum of 2:

 

 

 

 

The dice show a sum of 12:

 

 

 

 

The dice show a sum of 6:

 

 

 

 

The dice show a sum of 7:

 

 

 

 

Explain how you arrived at this last answer.


Team Tally Sheet

 

Each team should make a tally of the results for rolling the two dice.

 

Outcome                                  Tally                                                                  Total

1

 

 

2

 

 

3

 

 

4

 

 

5

 

 

6

 

 

7

 

 

8

 

 

9

 

 

10

 

 

11

 

 

12

 

 

13