 # Probability Tree Diagrams

In this worksheet, students use two-stage tree diagrams to answer probability questions. Key stage:  KS 4

Curriculum topic:  Probability

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

Difficulty level:   ### 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)

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) 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) 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) 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)

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)

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)

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)

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)

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)

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)

32/95
EDDIE SAYS
16/20 × 4/19 + 4/20 × 16/19
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial