Probability: past paper questions

Real questions on probability

The newest 20 of 92 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q7b[1]
   (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.See it on the paper →
2. 0580/11 · May/June 2026 · Q15a(ii)[1]
   15 (a) 60 people complete a survey about hobbles. 41 people like reading books ($R$). 31 people like cookery ($C$). 11 do not like reading books and do not like cookery. [Diagram: Venn diagram with universal set $\mathcal{U}$, two overlapping circles labelled $R$ and $C$] (ii) One of these 60 people is picked at random...See it on the paper →
3. 0580/12 · May/June 2026 · Q22a[2]
   22 A bag contains 7 pink blocks and 5 green blocks. Kay picks a block at random, notes its colour and puts it back in the bag. She does this a second time. (a) Complete the tree diagram. [Diagram: A tree diagram with two stages. The first stage is labelled "first block" and has two branches from a root: the upper branc...See it on the paper →
4. 0580/12 · May/June 2026 · Q22b[2]
   22 A bag contains 7 pink blocks and 5 green blocks. Kay picks a block at random, notes its colour and puts it back in the bag. She does this a second time. (b) Use the tree diagram to work out the probability that the two blocks are green.See it on the paper →
5. 0580/21 · May/June 2026 · Q9[1]

   1-mark question — its maths and diagrams are best seen on the paper.

   See it on the paper →
6. 0580/23 · May/June 2026 · Q2b[2]

   2-mark “Draw” question — its maths and diagrams are best seen on the paper.

   See it on the paper →
7. 0580/23 · May/June 2026 · Q27[4]
   27 Juan has a bag containing 2 red counters, 3 green counters and 5 blue counters. Juan picks two counters from the bag at random, without replacement. Find the probability that the two counters are different colours.See it on the paper →
8. 0580/43 · May/June 2026 · Q6b[1]
   The table shows the time 9 students each spent studying for a test and the number of errors each student made in the test. | study time (minutes) | 5 | 8 | 11 | 15 | 18 | 21 | 25 | 27 | 31 | |---|---|---|---|---|---|---|---|---|---| | number of errors | 35 | 34 | 30 | 25 | 24 | 20 | 13 | 9 | 6 | (b) What type of corr...See it on the paper →
9. 0580/43 · May/June 2026 · Q6c[1]

   1-mark “Draw” question — its maths and diagrams are best seen on the paper.

   See it on the paper →
10. 0580/43 · May/June 2026 · Q6d[1]
    The table shows the time 9 students each spent studying for a test and the number of errors each student made in the test. | study time (minutes) | 5 | 8 | 11 | 15 | 18 | 21 | 25 | 27 | 31 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | number of errors | 35 | 34 | 30 | 25 | 24 | 20 | 13 |...See it on the paper →
11. 0580/43 · May/June 2026 · Q9a[1]
    9 The table shows the marks of 100 students in a test. | mark | $0<x\le 20$ | $20<x\le 40$ | $40<x\le 60$ | $60<x\le 80$ | $80<x\le 100$ | | :--- | :---: | :---: | :---: | :---: | :---: | | frequency | 4 | 20 | 31 | 34 | 11 | (a) Write down the modal class. $\dots <x\le \dots$See it on the paper →
12. 0580/43 · May/June 2026 · Q9b[4]
    The table shows the marks of 100 students in a test. | mark | $0<x\le 20$ | $20<x\le 40$ | $40<x\le 60$ | $60<x\le 80$ | $80<x\le 100$ | | :--- | :---: | :---: | :---: | :---: | :---: | | frequency | 4 | 20 | 31 | 34 | 11 | (b) Calculate an estimate of the mean.See it on the paper →
13. 0580/22 · February/March 2026 · Q3b(i)[1]
    (b) Rishwan writes each of these numbers on a card. [Diagram: Seven cards in a row, each containing a number: $-50$, $-11$, $9$, $15$, $27$, $50$, $83$] Rishwan picks a card at random and replaces it. (i) Find the probability that he picks a natural number.See it on the paper →
14. 0580/01 · Specimen 2025 · Q17a[2]

    2-mark “Complete” question — its maths and diagrams are best seen on the paper.

    See it on the paper →
15. 0580/11 · October/November 2025 · Q14a[2]
    14 These are the ages, in **months**, of each of 12 children. | 11 | 27 | 8 | 10 | 26 | 17 | 28 | 12 | 9 | 13 | 22 | 12 | (a) Complete the stem-and-leaf diagram to show this information. | 0 | | 1 | | 2 | Key: $1\mid 7$ represents $17$ monthsSee it on the paper →
16. 0580/13 · October/November 2025 · Q26a[2]
    26 There are 2 sets of traffic lights on Li's journey to work. The probability he stops at the first set of traffic lights is $0.4$. The probability he stops at the second set of traffic lights is $0.7$. First set of traffic lights Second set of traffic lights [Diagram: A tree diagram. The first level has two br...See it on the paper →
17. 0580/13 · October/November 2025 · Q26b[2]
    26 There are 2 sets of traffic lights on Li's journey to work. The probability he stops at the first set of traffic lights is $0.4$. The probability he stops at the second set of traffic lights is $0.7$. First set of traffic lights [Diagram: A tree diagram starting with a root node. The first level has two branches: t...See it on the paper →
18. 0580/21 · October/November 2025 · Q20a[1]
    Bag A contains 5 white balls and 3 black balls. Bag B contains 3 white balls and 1 black ball. (a) Two balls are picked at random from bag B without replacement. Find the probability that both balls are black.See it on the paper →
19. 0580/21 · October/November 2025 · Q20b(i)[2]
    Bag A contains 5 white balls and 3 black balls. Bag B contains 3 white balls and 1 black ball. (b) The balls are replaced into bag B. Kyle picks a ball at random from each bag. (i) Complete the tree diagram. [Diagram: A tree diagram starting with Bag A. The first branch is 'white' with probability $\frac{5}{8}$. The...See it on the paper →
20. 0580/21 · October/November 2025 · Q20b(ii)[3]
    [Diagram: Two bags. Bag A contains 5 white balls and 3 black balls. Bag B contains 3 white balls and 1 black ball.] Bag A contains 5 white balls and 3 black balls. Bag B contains 3 white balls and 1 black ball. (b) The balls are replaced into bag B. Kyle picks a ball at random from each bag. (ii) Find the probability t...See it on the paper →

What examiners said

This problem-solving question involved ratios and a probability tree. Most candidates attempted this question. Relatively few candidates were awarded all 3 marks. Many were not correct in their conversion from ratio to fractions or decimals and proceeded to use the whole numbers 1 and 4 or the words red and green on the tree. Some candidates also put different probabilities on the second set of br...

— Examiner report, May/June 2025, 0580/11 Q19(a) (Cambridge)

This question was found to be challenging to many as it depended on values found in the previous part and, in fact, was the question where candidates had the most difficulties. Any follow through values had to be probabilities i.e., be between 0 and 1 for any marks to be awarded. As before, these values were often 1 and 4 but also, 2 and 8 were used. Of those who did attempt this part, the majorit...

— Examiner report, May/June 2025, 0580/11 Q19(b) (Cambridge)

Many correct answers were seen, although some candidates did not know how to attempt this question.

— Examiner report, May/June 2025, 0580/13 Q11(a) (Cambridge)