Edexcel IAL S1 Probability: exam questions and answers, notes and worked examples

Updated October 2026 · By Pete Bromfield

S1 probability uses Venn diagrams, tree diagrams and the rules $P (A \cup B) = P (A) + P (B) - P (A \cap B)$ and $P (A ∣ B) = \frac{P (A \cap B)}{P (B)}$ . Know the difference between mutually exclusive events ( $P (A \cap B) = 0$ ) and independent events ( $P (A \cap B) = P (A) P (B)$ ), and show the test when a question asks you to.

S1 · Statistics 1
Calculator allowed
3 worked examples
35 practice questions
Tested in 4 of the last 4 papers

Practise S1 probability →

Notes
Formulas
Worked examples
Mistakes
FAQ

S1 Probability notes

Venn diagrams and the addition rule

Fill a Venn diagram from the middle outwards. $P (A \cup B) = P (A) + P (B) - P (A \cap B)$ : with $P (A) = 0.5$ , $P (B) = 0.4$ and $P (A \cap B) = 0.2$ , $P (A \cup B) = 0.7$ and $P (A^{'} \cap B) = 0.2$ .

Mutually exclusive and independent events

Mutually exclusive: the events cannot happen together, so $P (A \cap B) = 0$ . Independent: one does not change the probability of the other, so $P (A \cap B) = P (A) \times P (B)$ . In the example above $0.5 \times 0.4 = 0.2 = P (A \cap B)$ , so $A$ and $B$ are independent.

Conditional probability

$P (A ∣ B)$ is the probability of $A$ given that $B$ has happened: $P (A ∣ B) = \frac{P (A \cap B)}{P (B)}$ . Above, $P (A ∣ B) = \frac{0.2}{0.4} = 0.5$ . On a Venn diagram, the "given" event becomes the whole sample space.

Tree diagrams

Multiply along branches, add between outcomes. Two counters are taken without replacement from a bag of 3 red and 5 blue: $P (both red) = \frac{3}{8} \times \frac{2}{7} = \frac{3}{28}$ and $P (one of each) = \frac{15}{28}$ . Given that both counters are the same colour, the probability that they are red is $\frac{3}{13}$ .

Key formulas

Union In the formula booklet: $P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Intersection In the formula booklet: $P (A \cap B) = P (A) P (B ∣ A)$
Conditional; independent Learn it: $P (A ∣ B) = \frac{P (A \cap B)}{P (B)}; P (A \cap B) = P (A) P (B)$

In the formula booklet = printed in Pearson's IAL formulae booklet, so know where to find it. Learn it = not printed there, so learn it by heart. All S1 formulas on one page (free PDF) →

S1 Probability worked examples

Each mark scheme is checked line by line before it is published here. M marks are for method, A marks for accurate answers that follow from them, B marks for independent results.

Worked example 1 · 3 marks · hard

A bag contains 5 green counters and 3 yellow counters. A counter is drawn at random, its colour is noted, and it is replaced. This is done 3 times in total. Find the probability that exactly 2 green counters are drawn.

Mark scheme

M1 for identifying the 3 ways to draw exactly 2 green counters: GGY, GYG, YGG.
M1 for calculating the probability of one such arrangement, e.g., $(\frac{5}{8}) \times (\frac{5}{8}) \times (\frac{3}{8}) = \frac{75}{512}$ .
A1 for multiplying by 3 to find the total probability: $\frac{225}{512}$ .

3 steps · 1 to fill in

Worked example 2 · 3 marks · hard

Three independent events $A$ , $B$ , and $C$ have probabilities $P (A) = 0.5$ , $P (B) = 0.4$ , and $P (C) = 0.3$ . Find the probability that exactly one of these events occurs.

Mark scheme

M1 for identifying the three scenarios: $(A \cap B^{'} \cap C^{'})$ , $(A^{'} \cap B \cap C^{'})$ , and $(A^{'} \cap B^{'} \cap C)$ .
M1 for calculating the probabilities of these scenarios: $(0.5 \times 0.6 \times 0.7) + (0.5 \times 0.4 \times 0.7) + (0.5 \times 0.6 \times 0.3)$ .
A1 for evaluating and summing: $0.21 + 0.14 + 0.09 = 0.44$ .

3 steps · 1 to fill in

Worked example 3 · 3 marks · hard

Given $P (A | B) = 0.5$ , $P (B) = 0.4$ , $P (A) = 0.3$ , find $P (B | A)$ .

Mark scheme

2 steps

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Common S1 probability mistakes

Mixing up exclusive and independent. Mutually exclusive events cannot both happen; independent events can, and do so with probability P(A) × P(B). Events with non-zero probabilities cannot be both.
Dividing by the wrong probability. In $P (A ∣ B)$ you divide by $P (B)$ , the event you are told has happened.
Not changing the second branch. Without replacement, the second set of branches has one fewer item in the denominator, and one fewer of the colour already taken.
Double counting in a Venn diagram. $P (A) + P (B)$ counts the overlap twice: subtract $P (A \cap B)$ once.

Every S1 mistake from the examiner reports, with the paper it came from →

S1 Probability FAQ

How do I show two events are independent?

Work out P(A) × P(B) and compare it with P(A ∩ B). If they are equal, the events are independent; say so in a sentence. Equivalently, show P(A | B) = P(A).

What does P(A | B) mean?

The probability that A happens given that B has happened. It equals P(A ∩ B) divided by P(B).

Is a calculator allowed in IAL S1?

Yes. A calculator is allowed in every Edexcel IAL maths unit, S1 included. Method marks are for the working you write down, so show it.

How long is the IAL S1 exam?

Each IAL maths unit, S1 included, is one written paper of 1 hour 30 minutes worth 75 marks.

How often does probability come up in S1?

In our mapping of the 4 Pearson S1 papers from June 2024 to June 2025, probability was tested in 4 of them (7 questions in all). Any topic can be examined in any series.

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More S1: Data and Summary Statistics · Representation of Data · Correlation and Regression · Discrete Random Variables · Normal Distribution

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Other units: IAL P1 · IAL P2 · IAL P3 · IAL P4 · IAL M1

Edexcel IAL S1 Probability: exam questions and answers, notes and worked examples

Try it first

S1 Probability notes

Venn diagrams and the addition rule

Mutually exclusive and independent events

Conditional probability

Tree diagrams

Key formulas

S1 Probability worked examples

Worked example 1 · 3 marks · hard

Mark scheme

Worked example 2 · 3 marks · hard

Mark scheme

Worked example 3 · 3 marks · hard

Mark scheme

Common S1 probability mistakes

S1 Probability FAQ

How do I show two events are independent?

What does P(A | B) mean?

Is a calculator allowed in IAL S1?

How long is the IAL S1 exam?

How often does probability come up in S1?

Next steps

Your S1 revision kit