B Tree Diagram Challenge PDF

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Name:

Class/Set:

Tree Diagrams - Independent Events

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1: A21 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?

____________________

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Answers: Tree Diagrams - Independent Events

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1:

1 2

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

4 5

pink

1

a) p(getting orange twice) = 5

1 5

=

b) p(not getting orange twice) = 1

1 25 1 5

1 5

d) p(getting different colours) = 51

4 5

24 = 25

4 5

4 5

4 5

1 5

1

c) p(getting the same colour twice) = 5

2:

1 5

1 5

17 = 25

= 258

1 2

0.9

0.1

Heads

Tails

a) p(getting Tails twice) = 0.1 b) p(not getting Tails twice) = 1

0.1 = 0.01 0.1

c)p(getting the same result twice) = 0.9 d) p(getting Heads exactly once) = 0.9

0.1 = 0.99 0.9 0.1

0.1 0.1

0.1 = 0.82 0.9 = 0.18

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Name:

Class/Set:

Tree Diagrams - Conditional Events

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1: A21 bag contains 10 counters with the letters of the word STATISTICS written on them. A counter is chosen at random and not replaced before choosing another one. Use this tree diagram to answer the following: 3 10

7 10

2 9

vowel

7 9

consonant

3 9

vowel

6 9

consonant

vowel

consonant

a) What is the probability of getting two consonants?

____________________ b) What is the probability of getting vowel at least once?

____________________ c) What is the probability of getting exactly one vowel?

____________________ d) What is the probability of not getting exactly one vowel?

____________________

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2: A21 drawer contains 8 green socks and 2 orange socks. A sock is chosen at random and not replaced before choosing another one. Use this tree diagram to answer the following: 8 10

2 10

7 9

green

2 9

orange

8 9

green

1 9

orange

green

orange

a) What is the probability of getting two orange socks?

____________________ b) What is the probability of getting green 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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Answers: Tree Diagrams - Conditional Events

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1:

1 2

3 10

7 10

vowel

7 9

consonant

3 9

vowel

6 9

consonant

vowel

consonant

6 9

7

a) p(getting two consonants) = 10

42 = 157 = 90 6 9

7 10

b) p(getting vowel at least once) = 1

7 9

3

c) p(getting exactly one vowel) = 10

d) p(not getting exactly one vowel) = 103 2:

2 9

8 = 48 90 = 15

7 10

3 9

2 9

7 10

42 = 90 = 157 6 9

48 = 158 = 90

1 2

8 10

2 10

7 9

green

2 9

orange

8 9

green

1 9

orange

green

orange

2

a) p(getting two orange socks) = 10 b) p(getting green at least once) = 1

1 9

= 902 = 451

2 10

1 9

88 = 90 = 44 45 8

c) p(getting two socks of different colours) = 10 8

d) p(getting two socks of the same colour) = 10

2 9 7 9

2 10 2 10

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8 9 1 9

16 32 = 45 = 90

58 = 29 = 90 45

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Name:

Class/Set:

Tree Diagrams - Algebra Problems

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1 1: Work out the following: 2

A box contains a total of 4 balls; some are purple and the rest are pink. A ball is chosen at random, then replaced before choosing again. If p(two purple balls) = 161 then find how many purple balls there are. purple purple pink purple pink pink

____________________ 1 out the following: 2: Work 2

A pencil case contains a total of 8 pencils; some are red and the rest are green. A pencil is chosen at random, then replaced before choosing again. 49 then find p(one pencil of each colour). If p(two red pencils) = 64 red red green red green green

____________________

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1 3: Work out the following: 2

A drawer contains a total of 8 socks; some are white and the rest are black. A sock is chosen at random and not replaced before choosing another one. If p(two white socks) = 281 then find how many black socks there are. white white black white black black

____________________ 1 out the following: 4: Work 2

A bag contains a total of 10 sweets; some are brown and the rest are grey. A sweet is chosen at random and not replaced before choosing another one. 28 then find p(two grey sweets). If p(two brown sweets) = 45 brown brown grey brown grey grey

____________________

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Answers: Tree Diagrams - Algebra Problems 1:

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1 2 n 4 n 4

purple

purple 4

n 4 n 4

4

n

pink purple

pink

4

4

n 4

pink

n

p(two purple balls) = 4n 4 = 161 so n2 = 1 or n = 1 The box contains 1 purple ball. 2:

1 2 n 8 n 8

red

red 8

n 8 n 8

8

n

green red

green

8

8

n 8

green

n 8

49 = 64 so n2 = 49 or n = 7 8 n 7 p(one pencil of each colour) = 2 n 8 8 = 32.

p(two red pencils) = 8n

3:

1 2 1

n 7 n 8

white 8

n 7 n 7

8

n 8

white black white

black 7

n 7

n 1 1 so n2 p(two white socks) = 8n 7 = 28 The drawer contains 6 black socks.

black

n = 2 or n = 2

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4:

1 2 1

n n 10

9

brown

10 n 9

grey

n 9

brown

brown

10 n 10

grey 9

n 9

p(two brown sweets) = 10n p(two grey sweets) = 10 10n

1

n 9

2 = 28 45 so n 9 n 1 9 = 45.

grey

n = 56 or n = 8

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