Probability: past paper questions

Real questions on probability

The newest 20 of 74 written questions. Open one to see it on the real paper.

1. 0980/11 · 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 →
2. 0980/11 · October/November 2025 · Q24c[1]
   24 $\mathcal{E}=\{\text{students in a year group}\}$ $H=\{\text{students who study History}\}$ $G=\{\text{students who study Geography}\}$ 80 students are in the year group. 40 students study History. [Diagram: A Venn diagram with a rectangle labeled $\mathcal{E}$. Inside are two overlapping circles labeled $H$...See it on the paper →
3. 0980/21 · October/November 2025 · Q20a[1]
   [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. (a) Two balls are picked at random from bag B without replacement. Find the probability that both balls are b...See it on the paper →
4. 0980/21 · 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 →
5. 0980/21 · 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 →
6. 0980/21 · October/November 2025 · Q20c[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. (c) The balls are replaced into their bags. Jo picks a ball at random from bag A and places it into bag B. Sh...See it on the paper →
7. 0980/22 · May/June 2025 · Q4a[1]
   [Diagram: Seven cards in a row, each containing a number: 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.See it on the paper →
8. 0980/22 · May/June 2025 · Q4b[1]
   Samira picks one of these cards at random and replaces it. (b) Samira repeats this 35 times. Calculate the number of times Samira is expected to pick an odd number.See it on the paper →
9. 0980/42 · May/June 2025 · Q16a[1]
   16 On any day, the probability that the weather will be sunny is $0.7$. (a) Find the probability that on any day the weather will not be sunny.See it on the paper →
10. 0980/42 · May/June 2025 · Q16b[3]
    16 On any day, the probability that the weather will be sunny is $0.7$. (b) When the weather is sunny, the probability that Rohit goes for a walk is $0.9$. When the weather is not sunny, the probability that Rohit goes for a walk is $0.2$. Find the probability that on any day Rohit goes for a walk.See it on the paper →
11. 0980/42 · May/June 2025 · Q22b[3]
    [Diagram: Venn diagram with universal set $\mathcal{E}$, set $G$ and set $H$. Region $G$ only contains 8. Intersection $G\cap H$ contains 13. Region $H$ only contains 7. Outside the sets contains 5.] $\mathcal{E}=\{\text{number of students in a class}\}$ $G=\{\text{number of students who study geography}\}$ $H = \...See it on the paper →
12. 0980/21 · October/November 2024 · Q10a[2]

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

    See it on the paper →
13. 0980/21 · October/November 2024 · Q10b[1]
    Jacinda plays a game with her friend. She can win, lose or draw the game. The probability that she wins the game is $0.28$. (b) Jacinda plays the game 150 times. Find the expected number of times that she wins.See it on the paper →
14. 0980/31 · October/November 2024 · Q6c(i)[3]
    (c) Mario sells ice creams in five flavours. The table shows the relative frequency of some of the ice cream flavours Mario sells. | | Vanilla | Chocolate | Strawberry | Coconut | Banana | |---|---|---|---|---|---| | Relative frequency | 0.34 | | 0.18 | 0.12 | | Mario sells three times as many chocolate ice creams as...See it on the paper →
15. 0980/31 · October/November 2024 · Q6c(ii)[2]
    (c) Mario sells ice creams in five flavours. The table shows the relative frequency of some of the ice cream flavours Mario sells. | | Vanilla | Chocolate | Strawberry | Coconut | Banana | |---|---|---|---|---|---| | Relative frequency | 0.34 | | 0.18 | 0.12 | | Mario sells three times as many chocolate ice creams as...See it on the paper →
16. 0980/41 · October/November 2024 · Q5a[1]
    A box contains 3 blue pens and 5 red pens. (a) Mia picks a pen from the box at random. Find the probability that she picks a red pen.See it on the paper →
17. 0980/41 · October/November 2024 · Q5b(i)[2]
    5 A box contains 3 blue pens and 5 red pens. (b) Mia puts the pen back into the box. She then picks a pen at random and replaces it. She then picks a second pen at random. (i) Complete the tree diagram. [Diagram: A tree diagram with two stages. The first stage is labelled "First Pen" and has two branches: "Blue" and "R...See it on the paper →
18. 0980/41 · October/November 2024 · Q5b(ii)[3]
    5 A box contains 3 blue pens and 5 red pens. (b) Mia puts the pen back into the box. She then picks a pen at random and replaces it. She then picks a second pen at random. (ii) Find the probability that Mia picks two pens that have the same colour.See it on the paper →
19. 0980/41 · October/November 2024 · Q5c[3]
    A box contains 3 blue pens and 5 red pens. (c) Mia now picks 3 of the 8 pens in the box at random without replacement. Find the probability that she picks 2 blue pens and 1 red pen.See it on the paper →
20. 0980/32 · May/June 2024 · Q4b(iii)[1]
    (b) 80 of the pets owned by the families are cats, rabbits or hamsters. The table shows the number of each pet. | Type of pet | Number of each pet | Pie chart sector angle | |---|---|---| | Cat | 38 | | | Rabbit | 28 | | | Hamster | 14 | | (iii) One of the pets is chosen at random. Find the probability that a rabbit...See it on the paper →

What examiners said

Candidates generally followed through from a correct part (a) to achieve this mark. Of those who did not achieve part (a), some managed to achieve the follow through mark, particularly when the 3 20 response for (a) was . Candidates who did not gain this mark often gave the answer rather 7 35 than 20 or they did not complete the calculation to reach an integer answer and gave their answer 140 as...

— Examiner report, May/June 2025, 0980/22 Q4(b) (Cambridge)

This part was answered well by many, but for others caused issues. Many did not recognise that it was necessary to use the weather probabilities from the previous part, and so only 0.9 and 0.2 were considered. Many multiplied these together to give an answer of 0.18. Some attempted to add values, often resulting in an answer of a probability that was greater than 1. Candidates should recognise tha...

— Examiner report, May/June 2025, 0980/42 Q16(b) (Cambridge)

This part was generally well answered, with the majority of candidates correctly starting from 28/80 and a smaller number from 126/360.

— Examiner report, May/June 2024, 0980/32 Q4(b)(iii) (Cambridge)