Fairness and Expected Outcomes worksheet
9 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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3 marks
A fair spinner has 5 equal sections. 1 of the sections is brown.
The spinner is spun 85 times.
(a)How many times would you expect the spinner to land on brown?
(b)How many times would you expect the spinner not to land on brown?
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3 marks
A fair spinner has 10 equal sections. 4 of the sections are orange.
Hafsa spins it 100 times.
(a)Work out how many times Hafsa would expect the spinner to land on orange.
(b)In fact the spinner landed on orange 39 times.
Explain why this does not mean the spinner is not fair.
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4 marks
A spinner has 17 equal sections.
3 of the sections are yellow, 7 are green and 7 are red.
(a)Is the spinner equally likely to land on each of the three colours?
Give a reason for your answer.
(b)Find the probability that the spinner lands on yellow.
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4 marks
In a game, a spinner with 12 equal sections is spun once. 3 of the sections are purple and 9 of the sections are orange.
Freya wins if the spinner lands on purple. Idris wins if the spinner lands on orange.
(a)Is this game fair? Give a reason for your answer.
(b)Explain how the spinner could be changed to make the game fair.
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2 marks
Work out how many turns there were.
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3 marks
A spinner has 8 equal sections, of which 2 are green.
Joel spins it 85 times.
(a)Work out how many times Joel would expect the spinner to land on green.
(b)Explain what your answer to part (a) means, given that the spinner cannot land on green a fraction of a time.
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6 marks
A church fete has a bottle tombola.
It costs \(50\)p for one go.
The probability that a player draws a winning ticket is \(\frac{1}{ 10 }\).
A player who wins is given \(£1.00\).
On one day the tombola has \(100\) goes.
(a)Find the total amount of money taken by the tombola that day.
(b)Find the total amount the stall would expect to pay out in prizes.
(c)Does the tombola expect to make a profit or a loss that day, and by how much?
You must show your working.
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3 marks
A spinner has \(12\) equal sections. Each section is either orange or yellow.
Anya spins the spinner \(30\) times.
She expects it to land on orange \(10\) times.
(a)Calculate how many of the \(12\) sections are orange.
(b)Calculate how many times she would expect it to land on yellow.
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4 marks
Which spinner would you expect to land on purple more often?
You must show your working.
Answers
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(a) \(17\)
(b) \(68\) -
(a) \(40\)
(b) An expected number is only what happens on average — a fair spinner will not land on orange exactly 40 times every 100 spins, and 39 is close to 40. -
(a) No — 3 sections are yellow, 7 are green and 7 are red, so the three colours do not have the same number of sections.
(b) \(\frac{ 3 }{ 17 }\) -
(a) No — Idris is more likely to win, because 9 of the 12 sections are orange and only 3 are purple.
(b) Recolour 3 of the orange sections purple, so that there are 6 of each colour. - \(125\)
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(a) \(21.25\)
(b) It is an average over many sets of 85 spins — any one set will give a whole number, usually 21 or 22. -
(a) \(£50.00\)
(b) \(£10.00\)
(c) A profit of £40.00 -
(a) \(4\ \text{sections}\)
(b) \(20\) - Ravi's spinner, with an expected \(63\) against \(54\)