8.1

Basic probability

Cambridge IGCSE Mathematics (0580)  · Unit 8: Probability  · 9 flashcards

Basic probability is topic 8.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 8 — Probability , alongside Combined events and Venn diagrams.  In one line: Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 5 definitions, 2 key concepts and 1 application card — covering the precise wording mark schemes reward.  Use the 5 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

Probability and express it as a mathematical value

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Example: the probability of flipping a fair coin and getting heads is 0.5.

Questions this Basic probability deck will help you answer

Definition Flip

Define probability and express it as a mathematical value.

Answer Flip

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Example: the probability of flipping a fair coin and getting heads is 0.5.
Key Concept Flip

Explain the difference between 'certain' and 'impossible' events in the context of probability.

Answer Flip

A 'certain' event has a probability of 1, meaning it will definitely happen. An 'impossible' event has a probability of 0, meaning it will never happen. Rolling a number less than 7 on a standard 6-sided die is certain; rolling a 7 is impossible.

Definition Flip

What is the sample space of an experiment, and how is it related to outcomes?

Answer Flip

The sample space is the set of all possible outcomes of an experiment. Each element in the sample space represents a single possible outcome.

Example: when flipping a coin, the sample space is {Heads, Tails}.
Key Concept Flip

A bag contains 3 red balls and 2 blue balls. What is the probability of selecting a red ball at random?

Answer Flip

The probability is calculated as (number of favorable outcomes) / (total number of outcomes). In this case, it's 3 (red balls) / 5 (total balls) = 0.6 or 60%.

Definition Flip

Describe what 'equally likely' outcomes mean in probability.

Answer Flip

'Equally likely' means that each outcome in the sample space has the same chance of occurring.

Example: in a fair coin toss, heads and tails are equally likely because each has a probability of 0.5.
Definition Flip

Distinguish between theoretical probability and experimental probability (relative frequency).

Answer Flip

Theoretical probability is what we expect to happen based on the nature of the event (

Example: probability of rolling a 3 on a fair die is 1/6). Experimental probability (relative frequency) is based on actual trials and is calculated as (number of times the event occurred) / (total number of trials).
Key Concept Flip

If an event is described as 'unlikely,' how does its probability value relate to 0 and 1?

Answer Flip

An 'unlikely' event has a probability value closer to 0 than to 1. While there is no precise cut-off, an unlikely event is generally considered to have a probability less than 0.5. For instance, drawing a specific card (

Example: Ace of Spades) from a standard deck of 52 cards is unlikely.
Key Concept Flip

Explain how relative frequency can be used to estimate probability in real-world scenarios.

Answer Flip

Relative frequency (experimental probability) provides an estimate of the true probability when theoretical probability is difficult or impossible to calculate. By repeating an experiment many times, the relative frequency tends to converge toward the theoretical probability, providing a useful estimate.

Definition Flip

What does 'even chance' mean in the context of probability?

Answer Flip

'Even chance' indicates that the probability of an event occurring is 0.5 or 50%. This means the event is just as likely to happen as it is not to happen. Tossing a fair coin and getting heads has an even chance.

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7.2 Vectors 8.2 Combined events

Key Questions: Basic probability

Define probability and express it as a mathematical value.

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Example: the probability of flipping a fair coin and getting heads is 0.5.
What is the sample space of an experiment, and how is it related to outcomes?

The sample space is the set of all possible outcomes of an experiment. Each element in the sample space represents a single possible outcome.

Example: when flipping a coin, the sample space is {Heads, Tails}.
Describe what 'equally likely' outcomes mean in probability.

'Equally likely' means that each outcome in the sample space has the same chance of occurring.

Example: in a fair coin toss, heads and tails are equally likely because each has a probability of 0.5.
Distinguish between theoretical probability and experimental probability (relative frequency).

Theoretical probability is what we expect to happen based on the nature of the event (

Example: probability of rolling a 3 on a fair die is 1/6). Experimental probability (relative frequency) is based on actual trials and is calculated as (number of times the event occurred) / (total number of trials).
What does 'even chance' mean in the context of probability?

'Even chance' indicates that the probability of an event occurring is 0.5 or 50%. This means the event is just as likely to happen as it is not to happen. Tossing a fair coin and getting heads has an even chance.

More topics in Unit 8 — Probability

Basic probability sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

8.2 Combined events

10 flashcards
8.3 Venn diagrams

10 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

probability chance likelihood certain impossible likely unlikely even chance outcome event sample space equally likely theoretical probability experimental probability relative frequency

Key terms covered in this Basic probability deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

Probability and express it as a mathematical value
The sample space of an experiment, and how is it related to outcomes
Describe what 'equally likely' outcomes mean in probability
Distinguish between theoretical probability and experimental probability (relative frequency)
What does 'even chance' mean in the context of probability

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How to study this Basic probability deck

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