This task is about predicting and calculating combinations.
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| Example | 2 | 3 | 1 | 3 | 4 | One pair (of 3's) |
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When five dice are thrown these are the seven different types of number combinations they can have on them: |
| Combination | Example |
| 1. All dice different | 1, 2, 4, 5, 6 |
| 2. One pair | 1, 2, 3, 3, 4 |
| 3. Two pairs | 2, 2, 5, 5, 6 |
| 4. One triple | 1, 4, 4, 4, 5 |
| 5. One triple + one pair | 2, 2, 3, 3, 3 |
| 6. Four dice the same | 3, 6, 6, 6, 6 |
| 7. Five dice the same | 4, 4, 4, 4, 4 |
| a) |
Using the combinations listed in the table, rank how often you would predict each one to occur, from most likely to least likely.
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i)
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most likely combination
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ii)
iii)
iv)
v)
vi)
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vii)
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least likely combination |
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| b) |
Throw the five dice 100 times and record your results in the table below.
You may work with a partner when you throw the dice.
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c)
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Use your results to calculate the probability of
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i)
ii)
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all dice different (i.e., combination number 1) __________
one pair (i.e., combination number 2) __________
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| d) |
What would you do to get a more accurate estimate of all the probabilities?
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e)
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In the table below:
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| f) |
Looking at the "Total" column, rank all the 7 combinations from the most likely to the least likely according to how often each type of combination actually occurred.
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| i) |
most common combination
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ii)
iii)
iv)
v)
vi)
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| vii) |
least common combination
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g)
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Compare the actual results in f) with what you predicted in a). Give the number(s) of the combination(s) for which your prediction was
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i)
ii)
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least accurate? ______________________________
most accurate? ______________________________ |
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