A coin is tossed 80 times and lands on heads 45 times. What is the relative frequency of heads?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Relative and expected frequencies Topical Past Papers.
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These Relative and expected frequencies Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Probability (E8.2) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Use relative frequency as an estimate of probability; calculate expected frequencies from probability and total trials.
A coin is tossed 80 times and lands on heads 45 times. What is the relative frequency of heads?
The probability of a spinner landing on red is 1/4. The spinner is spun 200 times. Find the expected number of times it lands on red.
[1 mark]A six-sided die is rolled 600 times. The number 6 appears 120 times. Use this data to estimate the probability of rolling a 6. State whether this suggests the die is biased.
[2 marks]A bag of 30 sweets contains red and green sweets only. The probability of picking a red sweet at random is 0.4. Find the expected number of red sweets.
[2 marks]Which of the following sample sizes would give the MOST reliable estimate of a probability?
A factory produces light bulbs. Testing 400 bulbs shows that 12 are faulty.
Use the data to estimate the probability that a randomly chosen bulb is faulty.
[1 mark]The factory produces 50 000 bulbs in a week. Estimate how many are likely to be faulty.
[2 marks]A biased four-sided die has probabilities P(1) = 0.2, P(2) = 0.35, P(3) = 0.25, P(4) = 0.2. The die is rolled 400 times. Find the expected number of times the die shows a 2.
[2 marks]A bag contains n sweets. The probability of picking a red sweet is 1/5. The expected number of red sweets is 14. Find the value of n.
[2 marks]