Candle combos

Candle combos

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
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Further Resources
This task is about possible outcomes, tree diagrams and probability.
Lynne had some candles in a box.
The height of each one was either tall or short.
The colour of each one was either yellow or red. 
 
The probability of the height being:
  • tall was 1⁄3
  • short was 2⁄3

The probability of the colour being:

  • yellow was 1⁄4
  • red was 3⁄4
The tree diagram below illustrates the probabilities of all the different combinations of height and colour of the candles.
 
a)
Complete the tree diagram by filling in all the blank boxes and circles with the correct word or probability.
One probability and one word have been written in for you.
 
 

 
b)
A candle is chosen without looking. What is the probability that the candle is ...
 
  i)
  
ii)
tall and yellow? __________
 
short and red? __________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
tree diagrams, probability, combinations
Description of task: 
Students complete a tree diagram to illustrate all the different combinations of height and colour of four candles and evaluate probabilities for some combinations.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

  

Y11 (03/2001)

2 marks
(for all boxes and circles correctly filled)
or
1 mark
('2/3' and 'short' correct)

a)

  
NOTE: The order of the tree diagram may differ in the last 2 rows.

2 marks – easy

1 mark – very easy

1 mark

1 mark

b)

i)

ii)

1/12 [accept 0.083]

6/12 or 1/2 [accept 0.5]

very difficult

very difficult
Diagnostic and formative information: 
 

Common error

Likely miscalculation

Likely reason

b)i)

   ii)

1/4
3/4

  

Using the probability of the colours only.

b)i)

   ii)

7/12
1 5/12

1/3 + 1/4
2/3 + 3/4

Adding rather than multiplying probabilities.

b)i)

   ii)

2/7
5/7

1/3 + 1/4 = = 2/7
2/3 + 3/4 = = 5/7

Adding rather than multiplying probabilities and incorrect method of addition.