Two coin game

Two coin game

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about the likelihood of events with two coins.
Keita threw two coins in the air. Each time Keita threw the coins, she tallied how they landed.
 
Outcome Tally Frequency
Head - Head

Head - Tail
 
Tail - Head
 
Tail - Tail
13

17

20

10

a)
 
How many times did Keita throw the two coins? __________
  
b)
What proportion of Keita's throws had an outcome of ...
 
 
i)
 
ii)
two heads? __________
 
at least one head? __________
 
c)
Draw an 'X' on the scale below to show the probability of Keita throwing two tails, based on her data in the table above.
 

 

Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
probability, fractions, experiments
Description of task: 
Students interpret a tally chart to answer questions about the proportion and probability of outcomes from a coin toss.
Curriculum Links: 
This resource can be used to help to identify students' understanding of writing likelihoods as fractions, decimals or percentages, and locating them on a number line in Probability.
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: 
  Y9 (04/1999)
a)   60 very easy
b) i) or 0.216 [accept if =] difficult
  ii) or or 0.83 [accept if =] very difficult
c)   difficult
Diagnostic and formative information: 
   Common error Likely reason
a) 4 Gives the number of categories in the table.
b) i)
    ii)		 13
50		 Gives the number of outcomes rather than the proportion (relative frequency).
b) ii) , 37 Gives the probability (or frequency) of 1 head rather than at least 1 head.
c)


c)

Gives theoretical probability for a fair coin rather than probability based on the data in the table.

Probability of 1 tail.