Knowledge organisers

Probability: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about probability on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Probability: How likely an event is, from 0 (impossible) to 1 (certain).
Relative frequency: The fraction of trials in which an outcome happened; an estimate of its probability.
Mutually exclusive: Events that cannot happen at the same time.
Independent events: One does not affect the other, so P(A and B) = P(A) × P(B).

Key formulas

Probability	\(P(\text{not }A)=1-P(A);\) \(\text{expected frequency}=n\times P(A)\)
Relative frequency	\(\frac{\text{frequency of the outcome}}{\text{number of trials}}\)
Mutually exclusive	\(P(A\text{ or }B)=P(A)+P(B)\)
Independent	\(P(A\text{ and }B)=P(A)\times P(B)\)
Conditional	\(P(A\mid B)=\frac{P(A\cap B)}{P(B)}\)
Tree diagrams: multiply along branches, add the outcomes you want
Without replacement: the second-branch probabilities change (one fewer item)

Worked example

A bag has 4 red and 6 blue beads. Two are taken without replacement. Find the probability that both are red.

P(first red) = 4/10
P(second red, given the first was red) = 3/9
Multiply along the branch: 4/10 × 3/9 = 12/90

Answer: 2/15

Common mistakes

Combined events: adding where you should multiply
Adding probabilities along a tree-diagram branch instead of multiplying

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Use the probability scale, calculate probabilities of single events and use P(not A) = 1 − P(A) to find missing probabilities.
Estimate probabilities using relative frequency from experiments and calculate expected frequencies for a given number of trials.
Find probabilities of combined events using sample space diagrams and Venn diagrams, including probabilities of unions and intersections.
Draw tree diagrams for combined events with and without replacement, and use them to calculate probabilities.
Calculate conditional probabilities from Venn diagrams, two-way tables and tree diagrams, such as the probability of A given that B has happened.
Calculate conditional probabilities from two-way tables, such as the probability that a student studies French given that they are in Year 11.

The printable sheet

Probability knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes — Probability knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Coordinate geometry · Geometry · Mensuration · Trigonometry · Transformations and vectors · Statistics · All Cambridge IGCSE Maths (0580) organisers