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
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2 |
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3 |
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4
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5 |
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6 |
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7 |
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8 |
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9 |
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10
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11 |
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12 |
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13 |
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Step 2 Answer Questions: |
What was the most frequent outcome? |
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What was the least frequent outcome? |
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How often did you roll an outcome of 1? |
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What do you think the likelihood is of rolling a 1? |
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How often did you roll an outcome of 12? |
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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
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The
outcome shows a sum of 2
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The
outcome shows a sum of 7
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The
outcome shows a sum which is an even number
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The
outcome shows a sum of 6
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The
outcome shows a sum of 1
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The
outcome on each die is the same number (doubles)
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The
outcome shows Òsnake eyesÓ (double ones)
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The
outcome shows a sum of 13
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Which outcome has the highest
probability of occurring? |
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Which outcome has the least probability
of occurring? |
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.
Each team should make a tally of the results for rolling the two dice.
Outcome Tally Total
1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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