IGCSE Maths Tree Diagrams and Conditional Probability Questions

Edexcel IGCSE 4MA1 Tree Diagrams and Conditional Probability: Exam Questions and Answers

Tree Diagrams and Conditional Probability questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.

3 worked examples

Higher tier · calculator allowed

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Start with one question on conditional probability. Stuck? Take a hint. No sign-in needed.

P (A) = \frac{1}{2}

P (B ∣ A) = \frac{3}{5}

and

P (B ∣ A^{'}) = \frac{1}{5}

. Find

P (A ∣ B)

Choose your answer · keys 1–4

\frac{2}{5}

\frac{3}{4}

\frac{3}{5}

\frac{3}{10}

What this topic covers

Probability 3: Probability Trees: Multiplying along branches of a tree diagram.
Conditional Probability 1: Tree Diagrams: Trees with 'without replacement' branches.
Conditional Probability 2: Formulas & Tables: P(A|B) — probability of A given B has happened.

Tree Diagrams and Conditional Probability worked examples

Worked example 1: Tree diagram with independent events

The probability of passing a test is 0.7. Two independent tests are taken. Find P(passing exactly one).

Solution

Pass then fail: $0.7 \times 0.3 = 0.21$ .
Fail then pass: $0.3 \times 0.7 = 0.21$ .
Total $0.42$ .

4 steps

Tip: Multiply along branches, add between outcomes.

Worked example 2: Without replacement

A bag has 3 red and 7 blue balls. Two are taken without replacement. Find P(both blue).

Solution

First blue: $\frac{7}{10}$ .
Second blue: $\frac{6}{9}$ (one blue has gone).
$\frac{7}{10} \times \frac{6}{9} = \frac{7}{15}$ .

4 steps · 1 to fill in

Tip: Both the numerator and denominator change on the second pick.

Worked example 3: Conditional probability from a table

Of 25 adults, 18 like tea; of 15 children, 9 like tea. A tea drinker is chosen at random. Find P(adult).

Solution

Tea drinkers: $18 + 9 = 27$ .
$P (adult ∣ tea) = \frac{18}{27} = \frac{2}{3}$ .

3 steps · 1 to fill in

Tip: 'Given' restricts you to one row or column.

Where students lose marks on tree diagrams and conditional probability

Examiner's noteProbability tables: dividing the remainder by the wrong number

Where marks are lost: Candidates find 1 − (given probabilities) correctly but divide by 2 instead of the number of outcomes sharing it; conditional probability in context is weak.

Examiners flagged this in 2 exam series (November 2023, June 2024). Summarised in our own words from Pearson Edexcel examiner reports. Read the full note →

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Questions students ask

Which Edexcel IGCSE Maths papers test tree diagrams and conditional probability?

Either Higher tier paper, 1H or 2H, can test tree diagrams and conditional probability: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more tree diagrams and conditional probability questions?

In the IGCSE student hub: Unit 6 (Statistics & Probability) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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Edexcel IGCSE 4MA1 Tree Diagrams and Conditional Probability: Exam Questions and Answers

Try it first

What this topic covers

Tree Diagrams and Conditional Probability worked examples

Worked example 1: Tree diagram with independent events

Solution

Worked example 2: Without replacement

Solution

Worked example 3: Conditional probability from a table

Solution

Where students lose marks on tree diagrams and conditional probability

Revise tree diagrams and conditional probability for the exam

Questions students ask

Practise tree diagrams and conditional probability with your progress saved

More Unit 6 topics: Statistics & Probability