Every introduction to probability question from 6 Cambridge IGCSE Mathematics (0580) past papers (Oct/Nov 2025 to May/June 2026), syllabus section 8.1. 8 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/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 Introduction to Probability past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q7
(a) Two fair 4-sided dice have faces numbered 1 to 4. The dice are thrown, and the numbers are multiplied to give a total. The table shows all the possible results.
| × | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 |
| 2 | 2 | 4 | 6 | 8 |
| 3 | 3 | 6 | 9 | 12 |
| 4 | 4 | 8 | 12 | 16 |
Find the probability the total is (i) 12 (ii) 5 (iii) a number that is less than 20.
(b) A biased 6-sided dice, numbered 1 to 6, is thrown. The probability of scoring the number 6 is 0.2. Work out the probability of scoring a number less than 6.
Show solution
- The table shows 4 × 4 = 16 equally likely outcomes.
- 12 appears 2 times in the table.
- P(12) = 2⁄16 = 1⁄8
- 5 does not appear anywhere in the table, so it is impossible.
- P(5) = 0
- The largest total in the table is 16, so every total is less than 20. It is certain.
- P(less than 20) = 1
- “Less than 6” means any score except 6.
- The probabilities of all outcomes add up to 1, so P(not 6) = 1 − P(6).
- P(less than 6) = 1 − 0.2 = 0.8
Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q7
A bag contains 8 discs numbered 1 to 8. A disc is picked at random. On a probability scale from 0 to 1, draw an arrow to show the probability that the number is (a) an even number, label it A (b) 9, label it B (c) less than 3, label it C.
Show solution
- The even numbers are 2, 4, 6 and 8. That is 4 out of 8.
- P(even) = 4⁄8 = 1⁄2, so draw arrow A at 0.5
- There is no disc numbered 9, so it is impossible. Draw arrow B at 0
- Numbers less than 3 are 1 and 2. That is 2 out of 8.
- P(less than 3) = 2⁄8 = 1⁄4, so draw arrow C at 0.25
Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q10
A bag contains red balls and green balls in the ratio red : green = 2 : 3. A ball is picked at random. Find the probability that it is a red ball.
Show solution
- The ratio 2 : 3 means that for every 2 red balls there are 3 green balls.
- So 2 out of every 2 + 3 = 5 balls are red.
- P(red) = 2⁄5
Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q7
A bag contains 6 red balls, 4 green balls and 2 blue balls. Zia takes a ball at random. A probability scale from 0 to 1 is marked with arrows A to G, equally spaced, so A = 0, B = 1⁄6, C = 1⁄3, D = 1⁄2, E = 2⁄3, F = 5⁄6 and G = 1. Which arrow shows the probability that (a) Zia takes a green ball (b) Zia takes a yellow ball (c) Zia does not take a blue ball?
Show solution
- There are 6 + 4 + 2 = 12 balls altogether.
- P(green) = 4⁄12 = 1⁄3, which is arrow C
- There are no yellow balls, so it is impossible: probability 0, which is arrow A
- Not blue means red or green: 6 + 4 = 10 balls. P = 10⁄12 = 5⁄6, which is arrow F
Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q14
A bag contains red, yellow, blue and green cards. P(red) = 0.53 and P(yellow) = 0.19. The probability of taking a blue card or a green card is in the ratio blue : green = 5 : 2. Complete the table.
Show solution
- All the probabilities add up to 1, so P(blue) + P(green) = 1 − 0.53 − 0.19 = 0.28.
- Share 0.28 in the ratio 5 : 2. There are 5 + 2 = 7 parts, so one part = 0.28 ÷ 7 = 0.04.
- Blue = 5 × 0.04 = 0.20 and green = 2 × 0.04 = 0.08.
- blue 0.20, green 0.08
Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q5
A fair 5-sided spinner has sections red, white, white, blue and red. The spinner is spun once.
(a) Write down the colour the spinner is least likely to land on. (b) Find the probability that it lands on white. (c) Find the probability that it does not land on red.
Show solution
- Count the sections: red 2, white 2, blue 1. There are 5 equal sections.
- Blue has the fewest sections (only 1): blue
- P(white) = number of white sections⁄total sections = 2⁄5
- Not red means white or blue: 2 + 1 = 3 sections.
- P(not red) = 3⁄5
- Check: P(red) = 2⁄5, and 2⁄5 + 3⁄5 = 1 ✓
0580 Introduction to Probability past paper questions: Extended (Papers 2 and 4)
Feb/Mar 2026 · Paper 4 · 0580/42/F/M/26 · Q6
A bag contains yellow, blue and red counters. Asif takes a counter at random. The probability that he takes a yellow counter is 27%. The probability that he takes a blue counter is 3⁄5. Find the probability that he takes a red counter.
Show solution
- Write both probabilities as decimals: 27% = 0.27 and 3⁄5 = 0.6.
- The three probabilities add up to 1.
- P(red) = 1 − 0.27 − 0.6 = 0.13
Oct/Nov 2025 · Paper 4 · 0580/43/O/N/25 · Q12
A vase contains flowers that are red or pink or white. Ruth picks a flower at random. The probability that it is not red is 0.9. The probability that it is not pink is 0.65. Find the probability that the flower is white.
Show solution
- P(not red) = 0.9, so P(red) = 1 − 0.9 = 0.1.
- P(not pink) = 0.65, so P(pink) = 1 − 0.65 = 0.35.
- All three probabilities add up to 1: P(white) = 1 − 0.1 − 0.35 = 0.55
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