Five dice game I

This task is about predicting and calculating combinations.
Practical Task
 
dice-2-md-120.png
  
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.
 
 
Combination Tally Frequency
1.   All dice different    
2.   One pair    
3.   Two pairs    
4.   One triple    
5.   One triple + one pair    
6.   Four dice the same    
7.   Five dice the same    
 
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?
 
 
 
 
 
Complete c) and d) by yourself and get your teacher to mark them.
 
e)
 
In the table below:
  • Record the results from at least four sets of 100 trials.
  • Add these up for each combination and put the total in the "Total'" column
 
Combination Group 1 Group 2 Group 3 Group 4 Total
1.   All dice different          
2.   One pair          
3.   Two pairs          
4.   One triple          
5.   One triple + one pair          
6.   Four dice the same          
7.   Five dice the same          
 
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? ______________________________