IB · Mathematics: Applications & Interpretation SL & HL · Statistics & probability

Poisson distribution: IB Mathematics: Applications & Interpretation questions with answers

Free Poisson distribution questions for IB Mathematics: Applications & Interpretation (SL & HL), HL only, part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.

Generate a full Poisson Distribution worksheet →All Statistics & probability questions

Poisson distribution practice questions

Question 1Structured · 6 marksA* challenge

The numbers of cars and lorries passing a point in one minute follow independent Poisson distributions with means 1.5 and 1.2.

(a)

Find the probability that exactly 4 vehicles pass in one minute.

[3]
(b)

Given that exactly 4 vehicles pass in a minute, find the probability that none of them is a lorry.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.149
total ~ Po(2.7) (M1)(A1)
0.149 A1
3
(b)0.0953
P(cars = 4) P(lorries = 0)P(total = 4) (M1)
correct values (A1)
0.0953 A1
3
Question 2Structured · 4 marks

The number of cars passing a checkpoint per minute follows a Poisson distribution with mean 2.5.

(a)

Find the probability that exactly 2 cars pass in one minute.

[2]
(b)

Find the probability that at least 10 cars pass in 3 minutes.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.257
Po(2.5) (M1)
0.257 A1
2
(b)0.224
Po(7.50): 1 − P(X ≤ 9) (M1)
0.224 A1
2
Question 3Structured · 5 marks

The number of calls to a helpline follows a Poisson distribution with a mean of 3 calls per ten minutes.

(a)

Find the probability of exactly 3 calls in a ten-minute period.

[2]
(b)

Find the probability of at least 7 calls in a 20-minute period.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.224
X ~ Po(3) (M1)
0.224 A1
2
(b)0.394
Y ~ Po(6) (A1)
1 − P(Y ≤ 6) (M1)
0.394 A1
3
Question 4Structured · 6 marksA* challenge

The numbers of cars and lorries passing a point in one minute follow independent Poisson distributions with means 2 and 3.

(a)

Find the probability that exactly 7 vehicles pass in one minute.

[3]
(b)

Given that exactly 7 vehicles pass in a minute, find the probability that none of them is a lorry.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.104
total ~ Po(5) (M1)(A1)
0.104 A1
3
(b)0.00164
P(cars = 7) P(lorries = 0)P(total = 7) (M1)
correct values (A1)
0.00164 A1
3
Question 5Structured · 4 marks

The number of cars passing a checkpoint per minute follows a Poisson distribution with mean 3.2.

(a)

Find the probability that exactly 2 cars pass in one minute.

[2]
(b)

Find the probability that at least 10 cars pass in 3 minutes.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.209
Po(3.2) (M1)
0.209 A1
2
(b)0.491
Po(9.60): 1 − P(X ≤ 9) (M1)
0.491 A1
2
Question 6Structured · 5 marks

The number of calls to a helpline follows a Poisson distribution with a mean of 1.8 calls per ten minutes.

(a)

Find the probability of exactly 2 calls in a ten-minute period.

[2]
(b)

Find the probability of at least 5 calls in a 20-minute period.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.268
X ~ Po(1.8) (M1)
0.268 A1
2
(b)0.294
Y ~ Po(3.6) (A1)
1 − P(Y ≤ 4) (M1)
0.294 A1
3

More Statistics & probability questions

Descriptive statisticsCorrelation & regressionProbabilityBinomial & normal distributionsχ² testst-testsMarkov chainsConfidence intervalsHypothesis testing & errors

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

Meet Riyaz →

Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in