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Cambridge IGCSE Maths (0580) · Topic 8: Probability · 8.3

Cambridge IGCSE Maths 0580 Combined Events and Tree Diagrams Questions

Combined Events and Tree Diagrams questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise combined events and tree diagrams →Combined Events and Tree Diagrams notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Combined Events and Tree Diagrams questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

Two fair six-sided dice are rolled and the scores are added.
Find the probability that the total is \(7\).

Show the worked answer
  1. A sample space diagram has \(36\) equally likely outcomes.
  2. Totals of \(7\): \((1,6), (2,5), (3,4), (4,3), (5,2), (6,1)\), so \(6\) outcomes.
  3. \(\frac{6}{36} = \frac{1}{6}\)

Answer: \(\frac{1}{6}\)

Question 2 Core non-calculator · easy

A fair coin is thrown and a fair six-sided dice is rolled.
Find the probability of a head and a \(6\).

Show the worked answer
  1. The events are independent: \(\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}\).

Answer: \(\frac{1}{12}\)

Question 3 Core calculator · easy · 2 marks

Two fair six-sided dice are rolled and their scores are added. Find the probability that the total is 7.

Show the answer and mark scheme
  • M1 6 outcomes out of 36, e.g. from a sample space diagram
  • A1 1/6 oe

Answer: \(\frac{1}{6}\)

Question 4 Core non-calculator · medium

Two fair spinners are each numbered \(1\), \(2\) and \(3\). Both are spun and the scores are added.
Find the probability that the total is \(4\).

Show the worked answer
  1. There are \(3 \times 3 = 9\) outcomes.
  2. Total \(4\): \((1, 3)\), \((2, 2)\), \((3, 1)\).
  3. \(\frac{3}{9} = \frac{1}{3}\)

Answer: \(\frac{1}{3}\)

Question 5 Core non-calculator · medium

\(A\) and \(B\) are independent events with \(P(A) = 0.3\) and \(P(B) = 0.6\).
Find (a) \(P(A \text{ and } B)\) (b) the probability that neither happens.

Show the worked answer
  1. (a) \(0.3 \times 0.6 = 0.18\)
  2. (b) \(P(\text{not } A) \times P(\text{not } B) = 0.7 \times 0.4 = 0.28\)

Answer: (a) \(0.18\) (b) \(0.28\)

Question 6 Core non-calculator · medium

The probability that it rains on any day is \(0.4\), independently of other days.
Use a tree diagram to find the probability that it rains on exactly one of Monday and Tuesday.

Show the worked answer
  1. Rain then dry: \(0.4 \times 0.6 = 0.24\). Dry then rain: \(0.6 \times 0.4 = 0.24\).
  2. \(0.24 + 0.24 = 0.48\)

Answer: \(0.48\)

Question 7 Core calculator · medium · 3 marks

A bag contains 4 red and 6 blue balls. A ball is taken at random, its colour is noted, and it is put back. Then a second ball is taken. Find the probability that

(a) both balls are red (b) one ball of each colour is taken.

Show the answer and mark scheme
  • B1 (a) 0.16 oe
  • M1 (b) 0.4 × 0.6 + 0.6 × 0.4
  • A1 (b) 0.48 oe

Answer: (a) \(0.16\) (b) \(0.48\)

Combined Events and Tree Diagrams questions: Extended

Extended content, for Papers 2 and 4. Core students can skip these.

Question 8 Extended non-calculator · hard

A bag holds \(5\) red and \(3\) blue counters. Two counters are taken at random without replacement.
Find the probability that both are red.

Show the worked answer
  1. First red: \(\frac{5}{8}\). Then \(4\) red are left out of \(7\): \(\frac{4}{7}\).
  2. \(\frac{5}{8} \times \frac{4}{7} = \frac{20}{56} = \frac{5}{14}\)

Answer: \(\frac{5}{14}\)

Question 9 Extended non-calculator · hard

A bag holds \(5\) red and \(3\) blue counters. Two counters are taken at random without replacement.
Find the probability that they are different colours.

Show the worked answer
  1. Red then blue: \(\frac{5}{8} \times \frac{3}{7} = \frac{15}{56}\). Blue then red: \(\frac{3}{8} \times \frac{5}{7} = \frac{15}{56}\).
  2. \(\frac{30}{56} = \frac{15}{28}\)

Answer: \(\frac{15}{28}\)

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test combined events and tree diagrams?

Combined Events and Tree Diagrams is on both tiers (syllabus 8.3), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more combined events and tree diagrams questions?

In the 0580 practice for topic 8 (Probability), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More probability questions