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Probability Tree Diagrams

In this worksheet, students use two-stage tree diagrams to answer probability questions.

'Probability Tree Diagrams' worksheet

Key stage:  KS 4

Curriculum topic:  Probability

Curriculum subtopic:  Calculate the Probability of Independent and Dependent Combined Events

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Tree diagrams are useful to answer probability questions where there is more than one event happening in succession.

 

Example

There are 7 red balls and 5 yellow balls in a bag.

I take one ball from the bag and keep it.

I then take another ball from the bag.

What is the probability of choosing two red balls?

(Give your answer as a reduced fraction in the form a/b)

 

Answer

Here is a tree diagram to show this information.

 

 

Notice how the probabilities change for the second choice depending on whether the first choice resulted in a red or a yellow ball.

P(Red Red) = 7/12 x 6/11 = 42/132 = 7/22

There are 7 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing two yellow balls?

 

(Give your answer as a reduced fraction in the form a/b)

 

There are 7 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing a yellow ball followed by a red one?

 

(Give your answer as a reduced fraction in the form a/b)

 

There are 7 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing a red ball followed by a yellow one?

 

(Give your answer as a reduced fraction in the form a/b)

 

There are 5 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing a red ball followed by a yellow one?

 

(Give your answer as a reduced fraction in the form a/b)

There are 16 boys and 10 girls in a class.

 

The teacher choses two children at random. 

 

What is the probability of choosing two girls?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

There are 16 boys and 10 girls in a class.

 

The teacher choses two children at random.

 

What is the probability of choosing two boys?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

There are 16 boys and 10 girls in a class.

 

The teacher choses two children at random.

 

What is the probability of choosing a boy and a girl?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

A farmer has 16 white sheep and 4 black sheep.

 

He randomly choses two sheep to shear.

 

What is the probability of choosing two black sheep?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

A farmer has 16 white sheep and 4 black sheep.

 

He randomly choses two sheep to shear.

 

What is the probability of choosing two white sheep?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

A farmer has 16 white sheep and 4 black sheep.

 

He randomly choses two sheep to shear.

 

What is the probability of choosing one of each colour?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

  • Question 1

There are 7 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing two yellow balls?

 

(Give your answer as a reduced fraction in the form a/b)

 

CORRECT ANSWER
5/33
EDDIE SAYS
5/12 × 4/11
  • Question 2

There are 7 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing a yellow ball followed by a red one?

 

(Give your answer as a reduced fraction in the form a/b)

 

CORRECT ANSWER
35/132
EDDIE SAYS
5/12 × 7/11
  • Question 3

There are 7 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing a red ball followed by a yellow one?

 

(Give your answer as a reduced fraction in the form a/b)

 

CORRECT ANSWER
35/132
EDDIE SAYS
7/12 × 5/11
  • Question 4

There are 5 red balls and 5 yellow balls in a bag.

 

I take one ball from the bag and keep it.  I then take another ball from the bag.

 

What is the probability of choosing a red ball followed by a yellow one?

 

(Give your answer as a reduced fraction in the form a/b)

CORRECT ANSWER
5/18
EDDIE SAYS
5/10 × 5/9 = 25/90
  • Question 5

There are 16 boys and 10 girls in a class.

 

The teacher choses two children at random. 

 

What is the probability of choosing two girls?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

CORRECT ANSWER
9/65
EDDIE SAYS
10/26 × 9/25
  • Question 6

There are 16 boys and 10 girls in a class.

 

The teacher choses two children at random.

 

What is the probability of choosing two boys?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

CORRECT ANSWER
24/65
EDDIE SAYS
16/26 × 15/25
  • Question 7

There are 16 boys and 10 girls in a class.

 

The teacher choses two children at random.

 

What is the probability of choosing a boy and a girl?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

CORRECT ANSWER
32/65
EDDIE SAYS
16/26 × 10/25 + 10/26 × 16/25
  • Question 8

A farmer has 16 white sheep and 4 black sheep.

 

He randomly choses two sheep to shear.

 

What is the probability of choosing two black sheep?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

CORRECT ANSWER
3/95
EDDIE SAYS
4/20 × 3/19
  • Question 9

A farmer has 16 white sheep and 4 black sheep.

 

He randomly choses two sheep to shear.

 

What is the probability of choosing two white sheep?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

CORRECT ANSWER
12/19
EDDIE SAYS
16/20 × 15/19
  • Question 10

A farmer has 16 white sheep and 4 black sheep.

 

He randomly choses two sheep to shear.

 

What is the probability of choosing one of each colour?

 

(Give your answer as a reduced fraction in the form a/b)

 

 

CORRECT ANSWER
32/95
EDDIE SAYS
16/20 × 4/19 + 4/20 × 16/19
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