igureMaths
Log in
Start free
←
Combined events & tree diagrams
Get dealt questions instead
→
Browse Combined events & tree diagrams
44 questions at your level
Difficulty
All
Level 1
Level 2
Level 3
Level 4
Level 5
Tree diagrams & independent events
17 questions
Lesson
Not started
Mark as done
A spinner can land on red, blue or yellow.
P
(
red
)
=
0.5
P(\text{red}) = 0.5
P
(
red
)
=
0.5
and
P
(
blue
)
=
0.2
P(\text{blue}) = 0.2
P
(
blue
)
=
0.2
.
The spinner is spun twice. The two spins are independent.
(a)
Work out the probability that the spinner lands on yellow on any one spin.
(b)
Work out the probability that the spinner lands on the
same colour
on both spins.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A bag contains
3
3
3
red counters and
7
7
7
white counters.
A counter is taken at random from the bag, its colour is recorded, and the counter is
put back
in the bag. This is done three times.
(a)
Work out the probability that all three counters taken are red.
(b)
Work out the probability that
exactly two
of the three counters taken are red.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
On any day, the probability that it rains in a town is
0.2
0.2
0.2
. Whether it rains on one day is independent of whether it rains on any other day.
Kofi wants the probability that it rains on
at least one
of the next two days. He writes:
P
(
at least one rainy day
)
=
0.2
+
0.2
=
0.4
P(\text{at least one rainy day}) = 0.2 + 0.2 = 0.4
P
(
at least one rainy day
)
=
0.2
+
0.2
=
0.4
(a)
Explain why Kofi's method is wrong.
(b)
Work out the correct probability that it rains on at least one of the next two days.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A biased spinner has five sections numbered
1
1
1
,
2
2
2
,
3
3
3
,
4
4
4
and
5
5
5
Leah spins the spinner
80
80
80
times.
The table gives the number of times the spinner lands on each number.
Number
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
Frequency
14
14
14
20
20
20
11
11
11
19
19
19
16
16
16
Leah is going to spin the spinner two more times.
(a)
Work out an estimate for the probability that the spinner will land on
4
4
4
both times.
(3 marks)
Marcus will spin the same spinner
n
n
n
times and use his results to get a better estimate of this probability.
(b)
What can you say about the value of
n
n
n
?
(1 mark)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
There are only
3
3
3
purple pens and
5
5
5
orange pens in a box.
Jay takes at random a pen from the box.
He records its colour and puts the pen back into the box.
Jay does this two more times.
Show that the probability that Jay takes at least two purple pens is
81
256
\frac{81}{256}
256
81
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Probability without replacement
17 questions
Lesson
Not started
Mark as done
A bag contains 5 white counters and 4 black counters.
Three counters are taken from the bag at random, without replacement.
(a)
Work out the probability that all three counters are white.
(b)
Work out the probability that all three counters are the same colour.
●●●●
●
Level 4
6 marks
Start
→
Mark as done
A bag contains 5 green counters and 7 yellow counters.
Two counters are taken from the bag at random, without replacement.
Jack writes:
P
(
both green
)
=
5
12
×
5
11
=
25
132
P(\text{both green}) = \frac{5}{12}\times\frac{5}{11} = \frac{25}{132}
P
(
both green
)
=
12
5
×
11
5
=
132
25
(a)
Explain what is wrong with the second fraction in Jack's working.
(b)
Work out the correct probability that both counters are green.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A tin contains 10 biscuits.
3 of the biscuits are chocolate and the other 7 are plain.
Three biscuits are taken from the tin at random, without replacement.
Work out the probability that at least one of the three biscuits is chocolate.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A bag contains only green counters and white counters.
The probability that a counter taken at random from the bag is green is
3
8
\frac{3}{8}
8
3
.
There are 15 white counters in the bag.
(a)
Show that there are 24 counters in the bag.
(b)
Two counters are taken from the bag at random, without replacement.
Work out the probability that the two counters are the same colour.
●●●●
●
Level 4
6 marks
Start
→
Mark as done
A bag contains
5
5
5
red counters and
3
3
3
blue counters and nothing else.
Kim takes at random two counters from the bag. She does
not
replace the first counter before taking the second.
Work out the probability that the two counters are different colours.
Give your answer as a fraction in its simplest form. (4 marks)
●●●●
●
Level 4
4 marks
Start
→
Conditional probability
10 questions
Lesson
Not started
Mark as done
A theatre sold
240
240
240
tickets for a play.
90
90
90
of the tickets were sold online and the rest were sold at the box office.
Every ticket was either a concession ticket or a full-price ticket. Altogether
44
44
44
of the
240
240
240
tickets were concession tickets.
Given that a ticket was sold online, the probability that it was a concession ticket is
2
15
\frac{2}{15}
15
2
.
(a)
Work out the number of concession tickets that were sold online.
(b)
One of the concession tickets is chosen at random.
Work out the probability that it was sold at the box office.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The two-way table shows information about
200
200
200
people who work in an office and how they travel to work.
Cycles to work
Does not cycle to work
Total
Aged under 30
24
24
24
56
56
56
80
80
80
Aged 30 or over
36
36
36
84
84
84
120
120
120
Total
60
60
60
140
140
140
200
200
200
(a)
One of the
200
200
200
people is chosen at random.
Write down the probability that this person cycles to work.
(b)
One of the people aged under
30
30
30
is chosen at random.
Work out the probability that this person cycles to work.
(c)
Ellie says that whether a person cycles to work is independent of their age group.
Is Ellie correct? You must justify your answer.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
Owen carried out a survey of
90
90
90
people.
He asked each person if they like apples (
A
A
A
), bananas (
B
B
B
) or grapes (
G
G
G
).
9
9
9
people like all three fruits.
23
23
23
people like apples and bananas.
11
11
11
people like apples and grapes but not bananas.
16
16
16
people like bananas and grapes.
44
44
44
people like grapes.
54
54
54
people like apples.
6
6
6
people like only bananas.
(a)
Complete the Venn diagram for this information.
ξ
A
B
G
(4 marks)
One of the
90
90
90
people is chosen at random.
Given that this person likes grapes,
(b)
find the probability that this person also likes bananas.
(2 marks)
●●●●
●
Level 4
6 marks
Start
→