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Tree Diagrams - Independent Events
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1: A12 spinner has 1 orange section and 4 pink sections (all equal).
It is spun twice.
Use this tree diagram to answer the following:
1
5
4
5
1
5
orange
4
5
pink
1
5
orange
4
5
pink
orange
pink
a) What is the probability of getting orange twice?
____________________
b) What is the probability of not getting orange twice?
____________________
c) What is the probability of getting the same colour twice?
____________________
d) What is the probability of getting different colours?
____________________
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1
2: The
probability of a biased coin landing Heads up is 0.9.
2
It is tossed twice.
Complete this tree diagram and hence answer the following:
Heads
Heads
Tails
Heads
Tails
Tails
a) What is the probability of getting Tails twice?
____________________
b) What is the probability of not getting Tails twice?
____________________
c) What is the probability of getting the same result twice?
____________________
d) What is the probability of getting Heads exactly once?
____________________
Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1
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1
3: The
probability of a certain type of TV being faulty is 0.29.
2
Two TVs are selected at random.
Complete this tree diagram and hence answer the following:
faulty
faulty
working
a) What is the probability of getting two faulty TVs?
____________________
b) What is the probability of not getting two faulty TVs?
____________________
c) What is the probability of getting exactly one faulty TV?
____________________
d) What is the probability of not getting exactly one faulty TV?
____________________
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1
4: One
drawer contains 2 blue socks and 7 purple socks.
2
A second drawer contains 3 blue socks and 2 purple socks.
A sock is chosen at random from each drawer.
Use this tree diagram to answer the following:
2
9
7
9
3
5
blue
2
5
purple
3
5
blue
2
5
purple
blue
purple
a) What is the probability of getting two blue socks?
____________________
b) What is the probability of getting purple at least once?
____________________
c) What is the probability of getting two socks of different colours?
____________________
d) What is the probability of getting two socks of the same colour?
____________________
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1
5: One
spinner has 5 black sections and 5 red sections (all equal).
2
Another spinner has 1 black section and 5 red sections (all equal).
Complete this tree diagram and hence answer the following:
black
black
red
black
red
red
a) What is the probability of getting red twice?
____________________
b) What is the probability of getting black at least once?
____________________
c) What is the probability of getting the same colour twice?
____________________
d) What is the probability of getting different colours?
____________________
Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1
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1
6: One
box contains 2 white balls and 6 yellow balls.
2
A second box contains 2 white balls and 5 yellow balls.
A ball is chosen at random from each box.
Complete this tree diagram and hence answer the following:
white
white
yellow
a) What is the probability of getting two yellow balls?
____________________
b) What is the probability of getting white at least once?
____________________
c) What is the probability of getting two balls of different colours?
____________________
d) What is the probability of getting two balls of the same colour?
____________________
Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1
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Answers: Tree Diagrams - Independent
Events
www..mathsprint.co.uk
1:
1
2
1
5
4
5
1
5
orange
4
5
pink
1
5
orange
4
5
pink
0.9
Heads
0.1
Tails
0.9
Heads
0.1
Tails
orange
pink
a) p(getting orange twice) = 15 × 15 = 251
b) p(not getting orange twice) = 1 − 15 × 15 = 24
25
c) p(getting the same colour twice) = 15 × 15 + 45 × 45 = 17
25
d) p(getting different colours) = 15 × 45 + 45 × 15 = 258
2:
1
2
0.9
0.1
Heads
Tails
a) p(getting Tails twice) = 0.1 × 0.1 = 0.01
b) p(not getting Tails twice) = 1 − 0.1 × 0.1 = 0.99
c) p(getting the same result twice) = 0.9 × 0.9 + 0.1 × 0.1 = 0.82
d) p(getting Heads exactly once) = 0.9 × 0.1 + 0.1 × 0.9 = 0.18
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3:
1
2
0.29
0.71
0.29
faulty
0.71
working
0.29
faulty
0.71
working
faulty
working
a) p(getting two faulty TVs) = 0.29 × 0.29 = 0.0841
b) p(not getting two faulty TVs) = 1 − 0.29 × 0.29 = 0.9159
c) p(getting exactly one faulty TV) = 0.29 × 0.71 + 0.71 × 0.29 = 0.4118
d) p(not getting exactly one faulty TV) = 0.29 × 0.29 + 0.71 × 0.71 = 0.5882
4:
1
2
2
9
7
9
3
5
blue
2
5
purple
3
5
blue
2
5
purple
blue
purple
a) p(getting two blue socks) = 29 × 35 = 456 = 152
13
b) p(getting purple at least once) = 1 − 29 × 35 = 39
45 = 15
5
c) p(getting two socks of different colours) = 29 × 25 + 79 × 35 = 25
45 = 9
4
d) p(getting two socks of the same colour) = 29 × 35 + 79 × 25 = 20
45 = 9
5:
1
2
5
10
5
10
1
6
black
5
6
red
1
6
black
5
6
red
black
red
5
a) p(getting red twice) = 105 × 56 = 25
60 = 12
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b) p(getting black at least once) = 1 −
5
10
7
× 56 = 35
60 = 12
c) p(getting the same colour twice) = 105 × 16 +
d) p(getting different colours) = 105 × 56 +
6:
5
10
5
10
1
× 56 = 30
60 = 2
1
× 16 = 30
60 = 2
1
2
2
8
6
8
2
7
white
5
7
yellow
2
7
white
5
7
yellow
white
yellow
15
a) p(getting two yellow balls) = 68 × 57 = 30
56 = 28
13
b) p(getting white at least once) = 1 − 68 × 57 = 26
56 = 28
11
c) p(getting two balls of different colours) = 28 × 57 + 68 × 27 = 22
56 = 28
17
d) p(getting two balls of the same colour) = 28 × 27 + 68 × 57 = 34
56 = 28
Free worksheet created by MATHSprint. Tree Diagrams - Independent Events:1
 MATHSprint, 2013