The Poisson distribution: past paper questions

Real questions on the poisson distribution

The newest 20 of 154 written questions. Open one to see it on the real paper.

1. 9709/63 · May/June 2026 · Q4a[1]

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

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2. 9709/63 · May/June 2026 · Q4b[3]

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

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3. 9709/63 · May/June 2026 · Q4c[2]

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

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4. 9709/63 · May/June 2026 · Q4d[5]

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

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5. 9709/61 · October/November 2025 · Q1a[2]
   The random variables $X$ and $Y$ have independent distributions $X\sim \text{Po}(3)$ and $Y\sim \text{Po}(2)$ respectively. (a) Find $\text{P}(2<X<5)$.See it on the paper →
6. 9709/61 · October/November 2025 · Q1b[3]
   The random variables $X$ and $Y$ have independent distributions $X\sim \text{Po}(3)$ and $Y\sim \text{Po}(2)$ respectively. (b) Find $P(X+Y>2)$.See it on the paper →
7. 9709/61 · October/November 2025 · Q3a[3]
   The data produced by a certain data entry firm always include a small number of incorrect characters that occur at random. The proportion of incorrect characters is denoted by $p$, and experience has shown that $p=0.0001$. A particular data set from the firm contains 14 500 characters, of which $X$ characters are inc...See it on the paper →
8. 9709/61 · October/November 2025 · Q3b[3]
   The data produced by a certain data entry firm always include a small number of incorrect characters that occur at random. The proportion of incorrect characters is denoted by $p$, and experience has shown that $p=0.0001$. A particular data set from the firm contains 14 500 characters, of which $X$ characters are inc...See it on the paper →
9. 9709/62 · October/November 2025 · Q1a[1]
   The number, $X$, of used computers donated to a charity has a constant average rate of 2.4 computers per week. (a) State a necessary condition for $X$ to have a Poisson distribution.See it on the paper →
10. 9709/62 · October/November 2025 · Q1b[3]
    The number, $X$, of used computers donated to a charity has a constant average rate of 2.4 computers per week. (b) Calculate the probability that the number of computers donated during a 4-week period is more than 6 and less than 9.See it on the paper →
11. 9709/62 · October/November 2025 · Q1c[4]
    The number, $X$, of used computers donated to a charity has a constant average rate of 2.4 computers per week. (c) Use a suitable approximating distribution to calculate the probability that more than 50 computers are donated during a 20-week period.See it on the paper →
12. 9709/62 · October/November 2025 · Q4b[1]
    An inspector believes that $18\%$ of cups made at a certain factory contain flaws. The factory owner claims that the true percentage is less than $18\%$. The inspector examines a random sample of $40$ cups and finds that $3$ of them contain flaws. (b) Explain why it would **not** be appropriate to use the Poisson appro...See it on the paper →
13. 9709/63 · October/November 2025 · Q1a[2]
    The random variables $X$ and $Y$ have independent distributions $X\sim \text{Po}(3)$ and $Y\sim \text{Po}(2)$ respectively. (a) Find $\text{P}(2<X<5)$.See it on the paper →
14. 9709/63 · October/November 2025 · Q1b[3]
    The random variables $X$ and $Y$ have independent distributions $X\sim \text{Po}(3)$ and $Y\sim \text{Po}(2)$ respectively. (b) Find $P(X+Y>2)$.See it on the paper →
15. 9709/63 · October/November 2025 · Q3a[3]
    The data produced by a certain data entry firm always include a small number of incorrect characters that occur at random. The proportion of incorrect characters is denoted by $p$, and experience has shown that $p=0.0001$. A particular data set from the firm contains 14 500 characters, of which $X$ characters are inc...See it on the paper →
16. 9709/63 · October/November 2025 · Q3b[3]
    The data produced by a certain data entry firm always include a small number of incorrect characters that occur at random. The proportion of incorrect characters is denoted by $p$, and experience has shown that $p=0.0001$. A particular data set from the firm contains 14 500 characters, of which $X$ characters are inc...See it on the paper →
17. 9709/61 · May/June 2025 · Q1[3]
    It is known that $1\%$ of houses in a certain area have a wind turbine. A random sample of 400 houses in this area is chosen for a survey on domestic heating. The number of houses in the sample that have a wind turbine is denoted by $X$. Use a suitable approximating distribution to find $P(X⩽3)$.See it on the paper →
18. 9709/61 · May/June 2025 · Q5a(i)[2]
    (a) The random variables $W$ and $X$ have the independent distributions Po(1.2) and Po(2.3) respectively. (i) Find $\text{P}(3⩽W+X⩽5)$.See it on the paper →
19. 9709/61 · May/June 2025 · Q5b[3]
    (b) The random variable $Y$ has the distribution $\text{Po}(\lambda )$, where $\lambda >0$. It is given that $\frac{5}{2}\text{P}(Y=3)+\text{P}(Y=4)=\text{P}(Y=5)$. Find the value of $\lambda$.See it on the paper →
20. 9709/62 · May/June 2025 · Q3a[1]
    The random variable $X$ has the distribution Po(15). (a) Write down an expression in terms of $e$ for $P(X=12).$See it on the paper →

What examiners said

This question was well attempted with most candidates correctly calculating 1- P(0, 1, 2). The most common errors were to calculate P(0, 1, 2) rather than 1– P(0, 1, 2) or to calculate 1– P(0, 1, 2, 3). It was important that the full Poisson expression was shown in order to fully justify the answer; candidates are advised to show all necessary working.

— Examiner report, February/March 2025, 9709/62 Q3(a) (Cambridge)

Many candidates correctly used 𝝀 = 4.5, though some used 𝝀 = 1.5. P(3, 4, 5) was generally calculated with or without the correct value for 𝝀. Again, the full Poisson expression was required.

— Examiner report, February/March 2025, 9709/62 Q3(b) (Cambridge)

This question was well attempted. Most solutions used the correct Normal distribution; the major errors noted were an incorrect or missing continuity correction or calculating the wrong tail probability.

— Examiner report, October/November 2023, 9709/62 Q1(a) (Cambridge)