AS Level · Mathematics 9709 · P5

AS Level Mathematics Paper 5 · Probability & Statistics 1 practice papers

50 marks · 1h 15m. Each generated paper follows the 9709 Paper 5 · Probability & Statistics 1 format, with the same number and style of questions as the real exam, and comes with a Cambridge-style mark scheme.

Generate Paper 5 · Probability & Statistics 1 →

Sample Paper 5 · Probability & Statistics 1 questions

Question 1Structured · 7 marksA* challenge

The lifetimes of a type of battery are normally distributed with mean 230 hours and standard deviation 19 hours.

(a)

Find the lifetime exceeded by 20% of batteries.

[3]
(b)

8 batteries are chosen at random. Find the probability that exactly 6 of them have lifetimes more than 235 hours.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)246 hours
z = 0.842 B1
μ + zσ M1
246 A1
3
(b)0.0395
p = 0.3962 B1
binomial with this p M1
28 × p6(1 − p)2 M1
0.0395 A1
4
Question 2Structured · 7 marksA* challenge

Bag X contains 5 red and 2 blue discs. Bag Y contains 6 red and 4 blue discs. A biased coin, with P(head) = 0.4, is thrown. If it shows a head, a disc is taken at random from bag X; otherwise a disc is taken at random from bag Y.

(a)

Find the probability that the disc is red.

[2]
(b)

Given that the disc is red, find the probability that it was taken from bag X.

[3]
(c)

Determine whether the events "the coin shows a head" and "the disc is red" are independent. Justify your answer.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.6457
sum of two products M1
0.6457 A1
2
(b)0.4425
P(X and red) ÷ P(red) M1
0.2857 ÷ 0.6457 A1
0.4425 A1
3
(c)not independent: P(red | head) = 0.7143 ≠ P(red) = 0.6457
valid comparison of probabilities M1
correct conclusion A1
2
Question 3Structured · 5 marks

The masses, X g, of apples are normally distributed with mean 47 and standard deviation 6.

(a)

Find P(X < 56).

[3]
(b)

Find P(56 < X < 57.2).

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.9332
Standardise M1
z = 1.500 A1
0.9332 A1
3
(b)0.0222
Φ(z2) − Φ(z1) M1
0.0222 A1
2
Question 4Structured · 2 marks

Find the number of different arrangements of the 7 letters in the word PEPPERS.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
420
7! ÷ (3! × 2!) M1
420 A1
2
Question 5Structured · 3 marks

For a set of 24 values, Σx = 549.6 and Σx2 = 13599.8. Find the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
mean 22.9, sd 6.5
22.9 B1
√(Σx2/n − mean2) M1
6.5 A1
3
Question 6Structured · 4 marks

Events A and B satisfy P(A) = 0.5, P(B) = 0.25 and P(A ∩ B) = 0.125.

(a)

Show that A and B are independent.

[1]
(b)

Find P(A ∪ B) and P(A | B′).

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)P(A)P(B) = P(A ∩ B)
0.5 × 0.25 = 0.125 B1
1
(b)0.625; 0.5
P(A ∪ B) = 0.625 B1
conditional formula M1
0.5 A1
3

Practise by topic

Pure Mathematics 1Pure Mathematics 2MechanicsProbability & Statistics 1

All AS Level Mathematics papers and topics

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 Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in