AS Level · Mathematics 9709 · Probability & Statistics 1

Discrete random variables: AS Level Mathematics questions with answers

Free Discrete random variables questions for AS Level Mathematics (9709), part of Probability & Statistics 1. Each question has the answer and the marking points an examiner would look for.

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Discrete random variables practice questions

Question 1Structured · 6 marksA* challenge

A bag contains 5 discs numbered 1 to 5. Two discs are taken at random, without replacement. The random variable X is the larger of the two numbers.

(a)

Draw up the probability distribution table for X.

[3]
(b)

Find E(X) and Var(X).

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)P(X = 2) = 110, P(X = 3) = 15, P(X = 4) = 310, P(X = 5) = 25
correct values of X B1
at least two correct probabilities M1
all correct A1
3
(b)E(X) = 4, Var(X) = 1
Σxp M1
Σx2p − (E(X))2 M1
both correct A1
3
Question 2Structured · 5 marks

A biased coin has probability 0.3 of showing heads. It is thrown 4 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
PartAnswer and marking pointsMarks
(a)binomial probabilities
binomial form M1
at least two correct A1
all correct A1
3
(b)1.2; 0.84
E(X) = 1.2 B1
Var(X) = 0.84 B1
2
Question 3Structured · 5 marks

The random variable X has the probability distribution shown.

x1234
P(X = x)0.230.260.26k
Table 3.1
(a)

Find k.

[1]
(b)

Find E(X) and Var(X).

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.25
0.25 B1
1
(b)E(X) = 2.53, Var(X) = 1.21
Σxp M1
2.53 A1
Σx2p − E(X)2 M1
1.21 A1
4
Question 4Structured · 6 marksA* challenge

A bag contains 6 discs numbered 1 to 6. Two discs are taken at random, without replacement. The random variable X is the larger of the two numbers.

(a)

Draw up the probability distribution table for X.

[3]
(b)

Find E(X) and Var(X).

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)P(X = 2) = 115, P(X = 3) = 215, P(X = 4) = 15, P(X = 5) = 415, P(X = 6) = 13
correct values of X B1
at least two correct probabilities M1
all correct A1
3
(b)E(X) = 143, Var(X) = 1.556
Σxp M1
Σx2p − (E(X))2 M1
both correct A1
3
Question 5Structured · 5 marks

A biased coin has probability 0.3 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
PartAnswer and marking pointsMarks
(a)binomial probabilities
binomial form M1
at least two correct A1
all correct A1
3
(b)0.9; 0.63
E(X) = 0.9 B1
Var(X) = 0.63 B1
2
Question 6Structured · 5 marks

A biased coin has probability 0.4 of showing heads. It is thrown 4 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
PartAnswer and marking pointsMarks
(a)binomial probabilities
binomial form M1
at least two correct A1
all correct A1
3
(b)1.6; 0.96
E(X) = 1.6 B1
Var(X) = 0.96 B1
2

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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