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44 questions at your level
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Level 5
Tree diagrams & independent events
17 questions
Lesson
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Bea rolls a fair six-sided dice numbered
1
1
1
to
6
6
6
. She also spins a spinner with
5
5
5
equal sections,
2
2
2
of which are green.
The roll of the dice and the spin of the spinner are independent.
(a)
Work out the probability that the dice lands on
6
6
6
and
the spinner lands on green.
(b)
Work out the probability that the dice does
not
land on
6
6
6
and
the spinner does
not
land on green.
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Level 3
5 marks
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The probability that Nia's train is on time on any morning is
0.85
0.85
0.85
. Whether the train is on time on one morning is independent of every other morning.
Nia catches the train on Monday morning and on Tuesday morning.
(a)
Work out the probability that the train is on time on
both
mornings.
(b)
Work out the probability that the train is on time on
exactly one
of the two mornings.
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Level 3
5 marks
Start
→
Mark as done
A bag contains
3
3
3
red counters and
2
2
2
blue counters.
A counter is taken at random and replaced. A second counter is then taken at random.
Work out the probability that the two counters are different colours. (3 marks)
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Level 3
3 marks
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The probability that Sam is late for school on any given day is
0.15
0.15
0.15
Whether Sam is late on one day is independent of whether he is late on any other day.
(a)
Work out the probability that Sam is late on both of the next two days. (2 marks)
(b)
Work out the probability that Sam is late on exactly one of the next two days. (2 marks)
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Level 3
4 marks
Start
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Probability without replacement
17 questions
Lesson
Not started
Mark as done
A box contains 7 red pens and 5 blue pens.
Two pens are taken from the box at random, without replacement.
(a)
Work out the probability that both pens are red.
(b)
Work out the probability that one pen is red and the other pen is blue.
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Level 3
5 marks
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Mark as done
A pencil case contains 9 pencils.
4 of the pencils are blue and the other 5 are black.
Kofi takes two pencils at random from the pencil case, without replacement.
Work out the probability that at least one of the two pencils is blue.
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Level 3
3 marks
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A bag contains
4
4
4
red counters and
6
6
6
blue counters. Two counters are taken at random without replacement.
(a)
Work out the probability that both counters are blue. [2]
(b)
Work out the probability that the counters are different colours. [2]
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Level 3
4 marks
Start
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Conditional probability
10 questions
Lesson
Not started
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A cycling club has
120
120
120
members.
45
45
45
of the members are aged under
18
18
18
and the rest are aged
18
18
18
or over.
27
27
27
of the members aged under
18
18
18
own a racing bike.
30
30
30
of the members aged
18
18
18
or over own a racing bike.
(a)
One of the members aged under
18
18
18
is chosen at random.
Work out the probability that this member owns a racing bike.
(b)
One of the members who owns a racing bike is chosen at random.
Work out the probability that this member is aged
18
18
18
or over.
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Level 3
5 marks
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The two-way table gives information about how the
150
150
150
pupils in Years 10 and 11 travel to school. One cell has not been filled in.
Walk
Cycle
Bus
Total
Year 10
24
24
24
15
15
15
36
36
36
75
75
75
Year 11
31
31
31
9
9
9
75
75
75
Total
55
55
55
24
24
24
71
71
71
150
150
150
(a)
Work out the number of Year 11 pupils who travel by bus.
(b)
One of the Year 11 pupils is chosen at random.
Work out the probability that this pupil cycles to school.
(c)
One of the pupils who cycles to school is chosen at random.
Work out the probability that this pupil is in Year 10.
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Level 3
5 marks
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400
400
400
adults in a town were asked whether they hold a driving licence and whether they own a car. The two-way table shows the results.
Owns a car
Does not own a car
Total
Holds a licence
210
210
210
70
70
70
280
280
280
Does not hold a licence
14
14
14
106
106
106
120
120
120
Total
224
224
224
176
176
176
400
400
400
(a)
One of the
400
400
400
adults is chosen at random.
Work out the probability that this adult owns a car
and
holds a licence.
(b)
One of the adults who owns a car is chosen at random.
Work out the probability that this adult holds a licence.
(c)
One of the adults who holds a licence is chosen at random.
Work out the probability that this adult owns a car.
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Level 3
6 marks
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40
40
40
people were asked whether they drink tea (
T
T
T
) and whether they drink coffee (
C
C
C
).
The Venn diagram shows the results.
ξ
9
T
C
13
9
9
One of the
40
40
40
people is chosen at random.
(a)
Work out the probability that this person drinks tea or coffee or both. (1 mark)
(b)
Work out the probability that this person drinks neither. (1 mark)
One of the people who drinks tea is chosen at random.
(c)
Work out the probability that this person also drinks coffee. (2 marks)
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Level 3
4 marks
Start
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