Probability: O-Level / IGCSE Maths (0580)

Syllabus C8.1, E8.1, C8.3, E8.3 · Strand 8 Probability

Questions: 3
Total marks: 17
Tier mix: 1 Core · 2 Extended

Probability measures how likely an event is to happen, on a scale from $0$ (impossible) to $1$ (certain). For equally likely outcomes, the probability of an event is $P(\text{event}) = \dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ . A key idea that runs through the whole topic is that the probabilities of all possible outcomes of an experiment add up to $1$ , so the probability that an event does not happen is $P(\text{not } A) = 1 - P(A)$ . This complement rule is often the quickest route to an answer.

This page also looks at combined events: situations involving more than one stage or more than one set. Tree diagrams are used to organise outcomes over successive steps: you multiply probabilities along the branches to find the chance of a particular path, and add the results of different paths to combine them. You will need to distinguish between events with replacement (where probabilities stay the same) and without replacement (where they change at the second stage). Venn diagrams help when outcomes belong to overlapping sets, letting you read off probabilities for intersections, unions, and complements at a glance.

Together these tools let you handle questions from a single dice roll up to multi-stage selections and grouped data. The worked examples below are original, written from the syllabus objective, and each is followed by a clear worked solution that shows the method exam-style.

Question 1

Structured Core 7 marks

Mira has a spinner divided into coloured sectors. When the spinner is spun once, it can land on red, blue, green or yellow. The probabilities of landing on some of the colours are shown in the table.

Colour	Red	Blue	Green	Yellow
Probability	0.15	0.4	0.25

(a) Complete the table by finding the probability that the spinner lands on yellow. [2]

(b) Write down the probability that the spinner lands on green. [1]

(d) Mira spins the spinner 200 times. Work out the expected number of times it lands on yellow. [2]

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Question 2

Structured Extended 8 marks

A fairground game uses a box containing 10 keyrings: 6 are silver and 4 are gold.

A player takes a keyring from the box at random, keeps it (it is not replaced), and then takes a second keyring from the box at random.

The situation can be modelled by a probability tree diagram with this structure:

First pick has two branches:
- Silver with probability $\tfrac{6}{10}$
- Gold with probability $\tfrac{4}{10}$
Second pick has two branches growing from each first‑pick branch, leading to the outcomes Silver–Silver, Silver–Gold, Gold–Silver, Gold–Gold. The probabilities on these second‑pick branches must be worked out, because one keyring has already been removed.

(a) Draw the tree diagram and label the probabilities on the four second‑pick branches. [2]

(b) Find the probability that both keyrings are silver. [2]

(d) Find the probability that the player takes at least one gold keyring. [1]

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Question 3

Multiple choice Extended 2 marks

A spinner has sections coloured red, blue and green. When spun once, the probability of landing on red is $\frac{2}{5}$ . Separately, a fair six-sided dice numbered $1$ to $6$ is rolled once. The spinner and the dice are operated independently. Find the probability that the spinner lands on red and the dice shows a number greater than $4$ .

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