Fairness and Expected Outcomes
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Either paper 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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Either paper 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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Either paper 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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Either paper 3 marks
The probability of tails when a biased coin is thrown is 0.3.
The coin is thrown 1450 times.
Work out the expected number of heads.
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Either paper 4 marks
Here are two spinners. On each spinner every section is equally likely.
Spinner A has 10 equal sections. 4 of them are red.
Spinner B has 6 equal sections. 1 of them is red.
You win a prize if the spinner lands on red.
(a)Which spinner gives the better chance of winning a prize? Show your working.
(b)Aisha uses spinner A 60 times. How many prizes would you expect Aisha to win?
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Either paper 2 marks
A spinner has 8 equal sections. 3 of the sections are white.
The spinner is spun a number of times. It is expected to land on white 27 times.
Work out how many spins there were.
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Either paper 3 marks
A spinner has 4 equal sections, of which 3 are orange.
Aisha spins it 65 times.
(a)Work out how many times Aisha would expect the spinner to land on orange.
(b)Explain what your answer to part (a) means, given that the spinner cannot land on orange a fraction of a time.
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Either paper 4 marks
In a game, a spinner with 10 equal sections is spun once. 3 of the sections are purple, 2 are orange and 5 are yellow.
Maya wins if the spinner lands on purple. Jonah wins if the spinner lands on orange or on yellow.
(a)Is this game fair? Give a reason for your answer.
(b)The spinner is spun 110 times.
Work out an estimate for the number of times Maya wins.
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Either paper 4 marks
There are 1500 students at a college.
A student is chosen at random.
(a)The probability that the student is taking a GCSE resit is \(0.06\).
How many of the students are taking a GCSE resit?
(b)The probability that the student is studying maths is \(0.68\).
The probability that the student is studying physics is \(0.51\).
Show that some students are studying maths and physics.
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Either paper 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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(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) \(\frac{ 3 }{ 17 }\) - \(1015\)
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(a) Spinner A
(b) \(24\) - \(72\)
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(a) \(48.75\)
(b) It is an average over many sets of 65 spins — any one set will give a whole number, usually 48 or 49. -
(a) No — Maya wins on 3 of the 10 sections and Jonah on 2 + 5 = 7, which is not the same, so the game is not fair.
(b) \(33\) -
(a) \(90\)
(b) The probabilities add to \(1.19\), which is more than 1, so the two groups must overlap: some students are studying both maths and physics. -
(a) \(£50.00\)
(b) \(£10.00\)
(c) A profit of £40.00
Takes a couple of seconds the first time a sheet is made.