O Level Mathematics: Probability Practice Questions (Cambridge 4024)

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs — Cambridge International holds copyright in its own papers. Use these alongside the official past papers available from your board.

Most questions practise a skill tested in the June 2025 papers. Questions marked (no calculator) are Paper 1 style; the rest allow a calculator, as in Paper 2. After each answer there is a tip and the real question to try next.

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Questions

1. (no calculator) A bag contains 12 balls: 5 red, 4 blue and the rest green. One ball is taken at random. Find the probability that it is (a) blue (b) not red. [2]

2. In a survey, the relative frequencies of students choosing football, tennis and other sports are 0.35, 0.25 and 0.1. Every other student chose cricket. (a) Find the relative frequency of cricket. (b) 400 students took part. How many chose tennis? [2]

3. (no calculator) A bag contains 7 red counters and 3 green counters. Two counters are taken at random without replacement. Find the probability that (a) both are red (b) one of each colour is taken. [4]

4. In a class of 30 students, 17 play football, 12 play basketball and 7 play neither. (a) How many play both? (b) A student is chosen at random. Find the probability that they play exactly one of the two sports. [4]

5. A fair six-sided dice is rolled 240 times. How many sixes would you expect? [1]

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Answers

1. (a) 4/12 = 1/3 [1]. (b) 7/12 [1].

Tip: “not red” is 1 − P(red), or count the balls that are not red.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 2.

2. (a) 1 − (0.35 + 0.25 + 0.1) = 0.3 [1]. (b) 0.25 × 400 = 100 [1].

Tip: relative frequencies of all outcomes add up to 1.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 6.

3. (a) 7/10 × 6/9 [1] = 7/15 [1]. (b) 7/10 × 3/9 + 3/10 × 7/9 [1] = 42/90 = 7/15 [1].

Tip: without replacement, both the number of that colour and the total go down by one for the second counter.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 13.

4. (a) 17 + 12 + 7 − 30 [1] = 6 [1]. (b) Football only = 11, basketball only = 6 [1], so P = 17/30 [1].

Tip: a Venn diagram with four regions helps; fill in the overlap first.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 9.

5. 240 × 1/6 = 40 [1].

Tip: expected frequency = probability × number of trials.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 6.

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Where marks are usually lost

• Not reducing the total for the second pick without replacement.
• Counting the overlap twice in a Venn diagram.
• Relative frequencies that do not add up to 1.