Probability & Statistics 1: AS Level Mathematics questions and answers
10 free AS Level Mathematics Probability & Statistics 1 questions written in the style of Cambridge Mathematics papers, each with its answer and mark scheme. 4 of them are A* challenge questions, built to catch the mistakes strong students still make.
This topic covers Representation of data, Permutations & combinations, Probability & the binomial distribution, Discrete random variables, The normal distribution. Work through the questions below, then generate a full Probability & Statistics 1 paper with a fresh set every time.
A game is played repeatedly until a player wins for the first time. The probability of winning any game is 0.3, independently.
(a)
Find the probability that the first win is on the 6th game.
[2]
(b)
Find the probability that more than 8 games are needed.
[2]
(c)
State the expected number of games needed for the first win.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.0504
geometric distribution: qk−1p M1 0.0504 A1
2
(b)
0.0576
q8M1 0.0576 A1
2
(c)
3.33
3.33 B1
1
Question 2Structured · 6 marksA* challenge
A committee of 5 people is to be chosen from 7 men and 6 women.
(a)
Find the number of different committees with at least 3 women.
[3]
(b)
Mr Khan and Ms Lee refuse to serve together. Find the number of committees with at least 3 women that do not include both of them.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
531
consider separate cases by number of women M1 at least two cases correct A1 531 A1
3
(b)
461
subtract committees containing both M1 70 with both A1 461 A1
3
Question 3Structured · 7 marksA* challenge
Bag X contains 4 red and 4 blue discs. Bag Y contains 2 red and 3 blue discs. A biased coin, with P(head) = 0.6, 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.
valid comparison of probabilities M1 correct conclusion A1
2
Question 4Structured · 7 marksA* challenge
The times, x minutes, taken by 20 students to complete a puzzle are summarised by Σx = 1360 and Σx2 = 94100. Another 14 students had mean time 59 minutes and standard deviation 10 minutes.
(a)
Find the mean and standard deviation of the times of the first group.
[2]
(b)
Find the mean and standard deviation of the times of all 34 students.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
68, 9
mean 68 B1 √(94100 ÷ 20 − 682) = 9 B1
2
(b)
64.3, 10.4
Σx for second group = 826 B1 Σx2 for second group = 50134 M1 combined mean 64.3 A1 combined variance formula M1 s.d. 10.4 A1
5
Question 5Structured · 5 marks
On average 10% of seeds of a type fail to germinate. 13 seeds are planted.
(a)
Find the probability that exactly 2 seeds fail to germinate.
[2]
(b)
Find the probability that fewer than 3 seeds fail to germinate.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.245
13C2 × 0.12 × 0.911M1 0.245 A1
2
(b)
0.866
P(0) + P(1) + P(2) M1 Correct terms A1 0.866 A1
3
Question 6Structured · 4 marks
Events A and B satisfy P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.3.
(a)
Show that A and B are independent.
[1]
(b)
Find P(A ∪ B) and P(A | B′).
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
P(A)P(B) = P(A ∩ B)
0.5 × 0.6 = 0.3 B1
1
(b)
0.8; 0.5
P(A ∪ B) = 0.8 B1 conditional formula M1 0.5 A1
3
Question 7Structured · 5 marks
A biased coin has probability 0.4 of showing heads. It is thrown 3 times. X is the number of heads.
(a)
Draw up the probability distribution table for X.
[3]
(b)
Find E(X) and Var(X).
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
binomial probabilities
binomial form M1 at least two correct A1 all correct A1
3
(b)
1.2; 0.72
E(X) = 1.2 B1 Var(X) = 0.72 B1
2
Question 8Structured · 6 marks
The masses, in grams, of 9 eggs are 19 26 26 30 34 50 56 58 58
(a)
Find the median and the interquartile range.
[3]
(b)
Calculate the mean and standard deviation.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
median 34; IQR 31
median 34 B1 quartiles M1 IQR 31 A1
3
(b)
39.7; 14.8
mean B1 Σx2/n − mean2M1 sd A1
3
Question 9Structured · 5 marks
The masses, X g, of apples are normally distributed with mean 50 and standard deviation 11.
(a)
Find P(X < 43.4).
[3]
(b)
Find P(43.4 < X < 61).
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.2743
Standardise M1 z = −0.600 A1 0.2743 A1
3
(b)
0.5671
Φ(z2) − Φ(z1) M1 0.5671 A1
2
Question 10Structured · 3 marks
For a set of 24 values, Σx = 708 and Σx2 = 21036. Find the mean and standard deviation.
What is in AS Level Mathematics Probability & Statistics 1?
In the 9709 syllabus, Probability & Statistics 1 covers Representation of data, Permutations & combinations, Probability & the binomial distribution, Discrete random variables, The normal distribution.
Where can I get Probability & Statistics 1 questions with mark schemes?
This page has 10 Probability & Statistics 1 questions with answers. For more, the free generator on mentorriyaz.in builds a new Probability & Statistics 1 paper with a full mark scheme each time you click.
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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.
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