Dice combinations III

Dice combinations III

Pencil and paper
Overview
Using this Resource
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Marking Student Responses
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Further Resources
This task is about finding all the possible combinations of outcomes for throwing two dice.

illustration: two dice

a)
When two dice are thrown there are 36 different combinations of numbers possible on the top faces of the two dice. Complete these tables, giving all the possible combinations when two dice are thrown.
 
Number on First Dice Number on Second Dice
1 1
1 2
1 3
1  
1  
1  
2  
2  
2  
2  
2  
2  
Number on First Dice Number on Second Dice
3  
3  
3  
3  
3  
3  
4   
4    
4   
4  
4  
4  
Number on First Dice Number on Second Dice
5  
5  
5  
5  
5  
5  
6  
6  
6  
6  
6  
6  

b)		  
Using the table, list all the combinations that add up to a total of 8.
   
 
i)
 
iv)
____ and ____
 
____ and ____
ii)
 
v)
____ and ____
 
____ and ____
 iii)
____ and ____
 
 
c)		  
List all the combinations that add up to a total of 11.
 
  i) ____ and ____ ii) ____ and ____    

d)		  
Two dice are thrown. What is the probability that the combination adds up to a total of 8 or 11? __________
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
combinations, probability
Description of task: 
Students complete a table to show all the combinations, and work out the probability, of numbers possible on the top faces of two dice. They then use the table to list combinations that total 8 and 11.
Curriculum Links: 
This resource can be used to help to identify students' understanding of finding all possible outcomes and expressing likelihoods as fractions.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y8 (07/1998)
a)

First 
Dice
1
1
1
1
1
1
2
2
2
2
2
2

Second
Dice
1
2
3
4
5
6
1
2
3
4
5
6

First
Dice
3
3
3
3
3
3
4
4
4
4
4
4

Second
Dice
1
2
3
4
5
6
1
2
3
4
5
6

First
Dice
5
5
5
5
5
5
6
6
6
6
6
6

Second
Dice
1
2
3
4
5
6
1
2
3
4
5
6
[Other orders are acceptable.]
very easy
b) 2, 6        3, 5        4, 4        5, 3        6, 2 easy
c) 5, 6        6, 5 very easy
d) 0.194 [accept 7/36 or 7 "successes" out of 36
or other equivalent probabilities/ratios/percentages]		 very difficult
Diagnostic and formative information: 
  Common error Likely reason
d) 7 Gives the number of combination that total 7 rather than probability.
d) 7/24, 7/70, 7/96 Wrong denominator but correct numerator.
d) 2/12 Assumes each total of two dice as equally likely.