Practise questions · Salam Academy

SA-9709-P5-PR-0032 marksL1 FoundationCalculatorConditional

P(A)=0.4

,

P(B)=0.5

and

P(A\cap B)=0.15

. Find

P(A\mid B)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0042 marksL1 FoundationCalculatorTree diagrams

A bag contains

5

red and

3

blue counters. Two are taken at random without replacement. Find the probability that both are red.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR2-0012 marksL1 FoundationCalculatorTree diagrams

A bag has

3

red and

7

blue balls. A ball is taken, its colour noted, and it is replaced; then a second ball is taken. Find the probability that the two balls are different colours.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR2-0041 markL1 FoundationCalculatorConditional

P(A\mid B)=0.4

and

P(B)=0.5

. Find

P(A\cap B)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-Q011 markL1 FoundationCalculatorConditional

P(A\mid B)

equals

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0053 marksL2 StandardCalculatorTree diagrams

From the same bag (

5

red,

3

blue), two counters are taken without replacement. Find the probability that they are different colours.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0074 marksL2 StandardCalculatorTree diagrams

The probability that it rains is

0.3

. If it rains, the probability that Sam is late is

0.4

; if not, it is

0.1

. Find the probability that Sam is late, and the probability that it rained given that Sam is late.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0113 marksL2 StandardCalculatorTree diagrams

A bag has

4

red and

6

blue balls. Three are taken without replacement. Find the probability that at least one is red.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0123 marksL2 StandardCalculatorConditional

P(A)=0.6

,

P(B)=0.5

and

P(A\cup B)=0.8

. Find

P(A\cap B)

and

P(A\mid B)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR2-0022 marksL2 StandardCalculatorConditional

Of

100

people,

40

are men, of whom

25

wear glasses, and

60

are women, of whom

20

wear glasses. A person who wears glasses is chosen at random. Find the probability that this person is a man.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0064 marksL3 ExamCalculatorConditional

From the bag of

5

red and

3

blue counters, two are taken without replacement. Given that at least one is red, find the probability that the first is red.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0093 marksL3 ExamCalculatorConditional

Two fair dice are thrown. Given that at least one shows a six, find the probability that the total is at least

10

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR2-0035 marksL3 ExamCalculatorConditional

2\%

of a population have a disease. A test is positive for

95\%

of people with the disease and for

10\%

of people without it. Find the probability that a randomly chosen person tests positive, and the probability that a person who tests positive has the disease (3 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PR-0145 marksL5 ExtensionCalculatorTree diagrams

Box X contains

3

red and

2

green balls; box Y contains

1

red and

4

green. A fair coin is thrown: heads, a ball is taken from X; tails, from Y. Given that the ball is red, find the probability that it came from box X.

Salam Academy Original Practice · Proposed mark scheme

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