Five dice game I
This task is about predicting and calculating combinations.
Practical Task  


Example  2  3  1  3  4  One pair (of 3's) 
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.


i)

most likely combination

____________________


ii)
iii)
iv)
v)
vi)


____________________
____________________
____________________
____________________
____________________


vii)

least likely combination 
____________________

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.




c)

Use your results to calculate the probability of


i)
ii)

all dice different (i.e., combination number 1) __________
one pair (i.e., combination number 2) __________


d) 
What would you do to get a more accurate estimate of all the probabilities?




e)

In the table below:



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.


i) 
most common combination

____________________  
ii)
iii)
iv)
v)
vi)

____________________
____________________
____________________
____________________
____________________


vii) 
least common combination

____________________


g)

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


i)
ii)

least accurate? ______________________________
most accurate? ______________________________ 