Every relative and expected frequencies question from 5 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 8.2. 5 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/23/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Probability past paper questions.
0580 Relative and Expected Frequencies past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q16
The probability that a team wins a match is 0.4.
(a) The team plays 20 matches. Work out the expected number of matches they win.
(b) The probability that the team loses is three times the probability that it draws. Complete the table of probabilities for win, lose and draw.
Show solution
- Expected number = probability × number of matches.
- 0.4 × 20 = 8
- The three probabilities add up to 1, so lose + draw = 1 − 0.4 = 0.6.
- Lose is three times draw, so lose : draw = 3 : 1. That is 4 parts.
- One part = 0.6 ÷ 4 = 0.15, so draw = 0.15 and lose = 3 × 0.15 = 0.45.
- lose 0.45, draw 0.15
- Check: 0.4 + 0.45 + 0.15 = 1 ✓
Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q15
The probability that Jai wins a game is 0.7. (a) Find the probability that he does not win a game. (b) Jai plays 50 games. Work out the number of games he is expected to win.
Show solution
- Winning and not winning are the only outcomes, so their probabilities add up to 1.
- P(not win) = 1 − 0.7 = 0.3
- Expected number = probability × number of games.
- 0.7 × 50 = 35
0580 Relative and Expected Frequencies past paper questions: Extended (Papers 2 and 4)
May/June 2026 · Paper 2 · 0580/23/M/J/26 · Q5
Reem has a six-sided spinner numbered 1 to 6. Reem spins the spinner 50 times. Her results are shown in the table.
| number on spinner | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| frequency | 8 | 7 | 5 | 9 | 12 | 9 |
(a) Write down the relative frequency of the spinner landing on the number 4.
(b) Reem spins the spinner 200 times. Find how many of these 200 spins are expected to land on the number 4.
Show solution
- Relative frequency = number of times it happened ÷ total number of trials.
- The spinner landed on 4 nine times out of 50 spins.
- Relative frequency = 9⁄50 (= 0.18)
- Expected number = relative frequency × number of spins.
- 9⁄50 × 200 = 9 × 4 = 36
Feb/Mar 2026 · Paper 2 · 0580/22/F/M/26 · Q3(b)
Rishwan writes each of these numbers on a card: −50, −11, 9, 15, 27, 50, 83. He picks a card at random and replaces it.
(i) Find the probability that he picks a natural number. (ii) He repeats this 140 times. Find the expected number of times that Rishwan picks a natural number.
Show solution
- Natural numbers are the positive whole numbers 1, 2, 3, … so negative numbers do not count.
- The natural numbers on the cards are 9, 15, 27, 50 and 83: 5 out of 7 cards.
- P(natural number) = 5⁄7
- Expected number = probability × number of picks.
- 5⁄7 × 140 = 140 ÷ 7 × 5 = 20 × 5 = 100
May/June 2025 · Paper 2 · 0580/22/M/J/25 · Q4
Cards numbered 1, 2, 3, 4, 5, 6, 7. Samira picks one of these cards at random and replaces it.
(a) Find the probability that she picks an odd number.
(b) Samira repeats this 35 times. Calculate the number of times Samira is expected to pick an odd number.
Show solution
- The odd numbers are 1, 3, 5 and 7. That is 4 out of 7 cards.
- P(odd) = 4⁄7
- Expected number = probability × number of picks.
- 4⁄7 × 35 = 35 ÷ 7 × 4 = 5 × 4 = 20
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