Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-9709-P6-PO2-0012 marksL1 FoundationCalculatorScaling λ

Customers arrive at a shop at random at an average rate of

6

per hour. Find the probability that exactly

1

customer arrives in a

20

-minute period, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-Q021 markL1 FoundationCalculatorSums

X\sim\text{Po}(2)

and

Y\sim\text{Po}(3)

are independent,

X+Y

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0033 marksL2 StandardCalculatorScaling λ

Calls arrive at a help desk at random at an average rate of

4

per hour. Find the probability of exactly

3

calls in a

30

-minute period, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0043 marksL2 StandardCalculatorSums

X\sim\text{Po}(1.5)

and

Y\sim\text{Po}(2.5)

are independent. Find

P(X+Y=3)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0072 marksL2 StandardCalculatorScaling λ

X\sim\text{Po}(\lambda)

and

P(X=0)=0.1

. Find

\lambda

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0113 marksL2 StandardCalculatorScaling λ

Faults occur in cloth at random at an average of

0.4

per metre. Find the probability of at least

2

faults in a

5

m length, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0023 marksL2 StandardCalculatorScaling λ

Breakdowns of a machine occur at random at an average rate of

0.8

per day. Find the probability of at most

3

breakdowns in a

7

-day week, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0033 marksL2 StandardCalculatorSums

X\sim\text{Po}(2)

and

Y\sim\text{Po}(1)

are independent. Find

P(X+Y\le1)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0043 marksL2 StandardCalculatorSums

A shop receives emails at random at

3

per hour and texts at random at

2

per hour, independently. Find the probability that it receives exactly

5

messages in total in one hour, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0052 marksL2 StandardCalculatorScaling λ

X\sim\text{Po}(\lambda)

and

P(X=0)=0.2

. Find

\lambda

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0063 marksL3 ExamCalculatorSums

X\sim\text{Po}(2.4)

and

Y\sim\text{Po}(1.6)

are independent. Find

P(X+Y\ge2)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0103 marksL4 ChallengingCalculatorScaling λ

X\sim\text{Po}(\lambda)

and

P(X=2)=P(X=3)

. Find

\lambda

Salam Academy Original Practice · Proposed mark scheme