A Level · Mathematics 9709 · Probability & Statistics 1

Discrete random variables: A Level Mathematics questions with answers

Free Discrete random variables questions for A 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 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

Part	Answer and marking points	Marks
(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 2Structured · 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 3Structured · 5 marks

The random variable X has the probability distribution shown.

x	1	2	3	4
P(X = x)	0.18	0.30	0.17	k

Table 3.1

(a)

Find k.

[1]

(b)

Find E(X) and Var(X).

[4]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.35 0.35 B1	1
(b)	E(X) = 2.69, Var(X) = 1.27 Σxp M1 2.69 A1 Σx²p − E(X)² M1 1.27 A1	4

Question 4Structured · 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

Part	Answer and marking points	Marks
(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 5Structured · 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

Part	Answer and marking points	Marks
(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

Question 6Structured · 5 marks

A biased coin has probability 0.2 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

Part	Answer and marking points	Marks
(a)	binomial probabilities binomial form M1 at least two correct A1 all correct A1	3
(b)	0.8; 0.64 E(X) = 0.8 B1 Var(X) = 0.64 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