Basic Probability: WJEC GCSE Higher June 2025 Unit 2 Q2

Higher June 2025 Unit 2 Q2

WJECHigherCurrent spec7 marksBasic Probability Solving Simple Equations

2. In this question you will be assessed on the quality of your organisation, communication and accuracy in writing.

A charity is organising a game using this fair spinner.

Fair spinner with five equal sections numbered 1, 2, 3, 4, 5

In the game, each player spins the spinner once.

100 players each pay £\(x\) to play the game once.
Each player who gets an even number on the spinner wins £3.

The charity expects to make a profit of £130.

Find the value of \(x\).
You must show all your working. [5 + 2 OCW]

Mark scheme

Scheme	Marks	Comments
(Expected prize money = ) \(\dfrac{2}{5}\) × 100 × (£)3 or equivalent	M2	May be seen or implied in later working. May be seen in stages. Award M1 for any one of the following: \(\dfrac{2}{5}\) × 100 or equivalent 40 (winners) (allow \(\dfrac{40}{100}\) or ‘40 out of 100’ or as a numerator in a fraction < 1) \(\dfrac{2}{5}\) × (£)3 or equivalent (£)1.2(0) FT ‘their derived or stated \(\dfrac{2}{5}\)’, provided ‘their \(\dfrac{2}{5}\)’ < 1 and number of winners is a whole number FT ‘their stated or derived number of winners’ × (£)3 provided the number of winners is a whole number.
(£)120(.00)	A1	CAO.
(Amount taken = £3 × 40 + £130 =) £250(.00)	A1	(£)120 + (£)130. FT ‘their (£)120’ + (£)130, provided at least M1 previously awarded.
(\(x\) = cost for playing the game once = (£3 × 40 + £130) ÷ 100 =) 2.5(0)	A1	Mark final answer. FT [‘their (£)120 + (£)130’] ÷ 100 provided that M1 is previously awarded. Allow M2 A1 A1 A1 for a correct embedded answer BUT only M2 A1 A1 A1 –1 (4 marks) if contradicted by \(x \neq 2.5\). If no marks, award SC1 for sight of \(\dfrac{2}{5}\) or equivalent.
Organisation and Communication.	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanation and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Accuracy of writing.	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc

Alternative method - working with groups of 5

Scheme	Marks	Comments
(Profit of each group of 5 people) = \(5x - 6\)	B1
\((5x - 6) \times 20 = 130\) or equivalent	M2	May be implied in later working (e.g. 6 × 20 + 130 and then 250 ÷ 100) Award M1 for \((5x - 6) \times 20\) or equivalent FT ‘their \((5x - 6)\)’ × 20, provided ‘their \((5x - 6)\)’ is in the form \(ax \pm b\).
\((100x - 120 = 130)\) or \((5x - 6 = 6{\cdot}5)\) \(100x = 250\) or \(5x = 12{\cdot}5\)	A1
(\(x\) =) 2.5(0)	A1	Mark final answer.

Alternative method 2 - working with winners and losers

Scheme	Marks	Comments
(40 winners) = \(40 \times (x - 3)\) or equivalent	B1
(60 losers) = \(60 \times x\) or equivalent	B1
\(40 \times (x - 3) + 60 \times x = 130\) \((100x - 120 = 130)\)	M1	May be implied in later working (e.g. 6 × 20 + 130 and then 250 ÷ 100). FT ‘their \(40 \times (x - 3)\)’ + ‘their \(60 \times x\)’ = 130, provided B1 previously awarded
\(100x = 250\)	A1
(\(x\) =) 2.5(0)	A1	Mark final answer.