Expected outcomes - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 18 exam-style questions on Expected outcomes for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

18 questions
1–5 marks each
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18 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

The probability that a tomato seed germinates is 0.86.
Ruby plants 450 of these seeds.

Work out an estimate for the number of seeds that germinate.

Model answer

Estimate = 0.86 × 450 = 387 seeds

Explanation

The expected number of times an event happens is its probability multiplied by the number of trials. Here each seed is one trial, so multiply 0.86 by 450. A common mistake is to divide by the probability instead of multiplying.

Mark scheme

1 mark
M1 for 0.86 × 450
oe
1 mark
A1 for 387
cao; correct answer with no working scores full marks

Question 2

3 marks

The table shows information about the probability that a biased four-sided spinner lands on each of the letters A, B, C and D.
The probability for D is missing from the table.

The spinner is spun 400 times.

Work out an estimate for how many more times the spinner will land on B than on D.

Table with columns "Letter", "A", "B", "C", "D". Letter: Probability; A: 0.15; B: 0.32; C: 0.4; D: .

Model answer

P(D) = 1 − (0.15 + 0.32 + 0.4) = 1 − 0.87 = 0.13
Expected number of Bs = 0.32 × 400 = 128
Expected number of Ds = 0.13 × 400 = 52
128 − 52 = 76 more times

Explanation

The four outcomes are mutually exclusive and cover every possibility, so their probabilities add up to 1 - this gives P(D). Each expected number is probability × 400. You can also find the difference of the probabilities first: (0.32 − 0.13) × 400 = 76.

Mark scheme

1 mark
M1 for 1 − (0.15 + 0.32 + 0.4) or for P(D) = 0.13
oe; correct answer with no working scores full marks
1 mark
M1 for 0.32 × 400 (= 128) and 0.13 × 400 (= 52), or for (0.32 − their 0.13) × 400
ft their P(D) if 0 < P(D) < 1
1 mark
A1 for 76
cao

Question 3

4 marks

At a school fair, there is a game with a fair spinner.
The spinner has 8 equal sections.
1 section is labelled £5, 2 sections are labelled £1 and the other 5 sections are labelled £0.

It costs £1.20 to play the game once.
A player spins the spinner once and wins the amount of money shown on the section it lands on.

150 people each play the game once.
Work out an estimate for the profit the school makes.

Model answer

Expected number of £5 wins = \(\frac{1}{8} \times 150 = 18.75\)
Expected number of £1 wins = \(\frac{2}{8} \times 150 = 37.5\)
Expected prize money = 18.75 × £5 + 37.5 × £1 = £93.75 + £37.50 = £131.25
Money taken = 150 × £1.20 = £180
Estimated profit = £180 − £131.25 = £48.75

Explanation

Use the probabilities to estimate how many times each prize is won, and so the total prize money; the profit is the money taken minus the prize money paid out. Expected numbers such as 18.75 are fine in the working because they are averages. Equivalently, the expected prize per game is £0.875, so the school expects to make £0.325 per game.

Mark scheme

1 mark
P1 for P(£5) = \(\frac{1}{8}\) and P(£1) = \(\frac{2}{8}\) used, e.g. \(\frac{1}{8} \times 150\) (= 18.75) or \(\frac{2}{8} \times 150\) (= 37.5)
oe
1 mark
P1 for the expected prize money, e.g. 18.75 × 5 + 37.5 × 1 (= 131.25), or \(\frac{1}{8} \times 5 + \frac{2}{8} \times 1\) (= 0.875 per game)
oe
1 mark
P1 for 150 × 1.20 (= 180) − their 131.25, or (1.20 − their 0.875) × 150
ft their prize money
1 mark
A1 for £48.75
accept £48.75 or £49 if 48.75 seen; correct answer with no working scores full marks

Question 4

5 marks

An insurance company sells 8600 phone insurance policies for one year.
For each policy, the probability that a claim is made during the year is 0.035.
The mean cost of a claim to the company is £2400.

The company wants to make a profit of £100 000 from these policies.
All the policies cost the same amount.

Work out how much the company should charge for each policy.
Give your answer to the nearest penny.

Model answer

Expected number of claims = 0.035 × 8600 = 301
Expected cost of claims = 301 × £2400 = £722 400
Money needed = £722 400 + £100 000 = £822 400
Charge per policy = £822 400 ÷ 8600 = £95.627...
= £95.63 (to the nearest penny)

Explanation

Use the probability to estimate how many claims will be made, then the total cost of those claims. The income from the policies must cover the claims and the profit, so divide that total by the number of policies. A common mistake is to forget to add the profit, or to divide only the profit by 8600.

Mark scheme

1 mark
P1 for 0.035 × 8600 (= 301) expected claims
oe
1 mark
P1 for their 301 × 2400 (= 722 400)
or 0.035 × 2400 (= 84) expected cost per policy
1 mark
P1 for their 722 400 + 100 000 (= 822 400)
or 100 000 ÷ 8600 (= 11.627...) added to their 84
1 mark
P1 for their 822 400 ÷ 8600
ft their total
1 mark
A1 for £95.63
cao (95.627...); correct answer with no working scores full marks

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