Two zone spinner

Two zone spinner

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about probablility as a fraction or percentage. 

spinner

The arrow on the spinner is equally likely to point to the black half of the circle as it is to the white half.
Write each probability as a fraction or as a decimal.

Question 1Change answer

a) What is the probability that in the first spin the arrow lands on the white? 

Question 1Change answer

b)  What is the probability that in two spins the arrow lands so that
i)   both are black?   
ii)  the first is white and the second is black?   
iii) one is black and one is white?   

Question 2Change answer

c)  What is the probability that in the first four spins the arrow always lands on the white?
Task administration: 
This task is completed with pencil and paper or online.
Level:
5
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
probability, spinners
Description of task: 
Students use a picture of a spinner to calculate the probability of the arrow pointing to the black or white portion of a card.
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: 
 

Y10 (06/2000)

a)

  

0.5 or 1/2 or 50%

very easy

b)

i)
ii)
iii)

 0.25 or 1/4 or 25%
0.25 or 1/4 or 25%
0.5 or 1/2 or 50%

3 correct - very difficult
2 correct - difficult
1 correct - moderate

c)

i)

0.0625 or 1/16

very difficult
Accept equivalent fractions, or correct percentages.
Diagnostic and formative information: 
  

Common error

Likely calculation

Likely reason

b)

i)    or
 
ii)  or

= =
or
+ =

Sees 2 favourable outcomes out of 4 possible ones.
 
Adding rather than multiplying probabilities (plus incorrect addition).

c)

+ + + =

Adding rather than multiplying probabilities (plus incorrect addition).
Next steps: 
Extension:
Work out the probabilities for a) b) and c) for a spinner with P (black) = 0.25 and P (white) = 0.75.
 
Answers:   a) 3/4   b) i) 1/16   ii) 3/16   iii) 6/16   c) 81/256