# Use Frequency Trees

In this worksheet, students practise drawing and using frequency trees to solve probability problems.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Basic Probability and Experiments

Difficulty level:

### QUESTION 1 of 10

There are a number of ways to record multiple event probabilities, you can use for example  probability trees, sample space diagrams  or two way tables.

Today, we'll look at another type of diagram that can be used to record the outcomes for two or more events. Frequency trees.

Frequency trees are just used to classify information. Let's look at a couple to illustrate this point.

Example 1:

60 people are members of a gym. Of these 45 are male.

Draw a frequency tree to show this information.

We can see here that there is only 1 piece of information (the gender) so we only need a one branch frequency tree. Each 'branch' of the tree will have one of the options.

We can now start building our tree. We know that there are 60 people in total, so we place this information in the first space.

We also know that we have 45 males.

Which means we must have 15 females.

Example 2: In a class of 32 students, 18 are boys of which 7 are left handed.

There are 15 left handed people in the class all together.

If I pick a student at random, what is the probability it is a right handed girl.

We can see there are 2 options here, Gender and left handed/right handed. This means we need a two level frequency tree,

Once we have the structure. We can start working out what goes where.

We have 32 students, if 18 are male, this means 14 must be female,

We are told that 7 of the boys are left handed so 11 of the boys must be right handed

We are also told that there are 15 left handed people alltogether, if 7 boys are left handed then 8 girls must be

This leaves us with 6 right handed girls.

We can now finally answer our probability question.

We know we have 6 right handed girls out of the 32 students which gives a probability of...

 6 32
=
 3 16

Freqeuency trees are used to...

If there are 30 students in a class and 14 are male. How many girls are in the class?

100 people are members of a cycling club.

40 are female.

17 of the female riders are under 16

35 of the male riders are under 16.

100 people are members of a cycling club.

40 are female.

17 of the female riders are under 16

35 of the male riders are under 16.

 Value D E F G

100 people are members of a cycling club.

40 are female.

17 of the female riders are under 16

35 of the male riders are under 16.

What is the probability an athlete chosen at random will be a male rider over the age of 16?

32 pupils are in a class. Of the 20 boys, 11 are left handed.

Half the girls are left handed,

32 pupils are in a class. Of the 20 boys, 11 are left handed.

Half the girls are left handed,

 Value D E F G

32 pupils are in a class. Of the 20 boys, 11 are left handed.

Half the girls are left handed,

If I pick a student at random, which of these probabilities describe picking a right handed girl?

6/32

6/12

1/2

3/16

120 members of a swimming club. 56 are male.

1/4 of the female members are over 40

1/14 of the males are over 40

 Value A B C D E F G

120 members of a swimming club. 56 are male.

1/4 of the female members are over 40

1/14 of the males are over 40

What is the probability that I pick a swimmer over 40 if I pick someone at random?

• Question 1

Freqeuency trees are used to...

EDDIE SAYS
Frequency trees are used to put things into order so we can use the information. We call this sorting or classifying. (These mean exactly the same thing in Maths)
• Question 2

If there are 30 students in a class and 14 are male. How many girls are in the class?

16
EDDIE SAYS
There are only two options, Male or Female. This means the two numbers on the right have to add up to 30. 30 - 14 = 16
• Question 3

100 people are members of a cycling club.

40 are female.

17 of the female riders are under 16

35 of the male riders are under 16.

EDDIE SAYS
We always start with the first box. This has to be the total for the question. In this case, that is 100 riders. We are also told that 40 are female, this means 60 have to be male.
• Question 4

100 people are members of a cycling club.

40 are female.

17 of the female riders are under 16

35 of the male riders are under 16.

 Value D E F G
EDDIE SAYS
We already know we have 40 females. If we know that we have 17 riders under 16, we must have 23 that are over 16 In the same vein, we have 35 male under 16 riders so if we have 60 overall, we must have 25 that are over 16
• Question 5

100 people are members of a cycling club.

40 are female.

17 of the female riders are under 16

35 of the male riders are under 16.

What is the probability an athlete chosen at random will be a male rider over the age of 16?

1/4
EDDIE SAYS
We have 25 male riders over the age of 16. This gives a probability of 25/100 which cancels down to ...
• Question 6

32 pupils are in a class. Of the 20 boys, 11 are left handed.

Half the girls are left handed,

EDDIE SAYS
We always start with the first box. This has to be the total for the question. In this case, that is 32 students We are also told that 20 are male, this gives us 12 female students.
• Question 7

32 pupils are in a class. Of the 20 boys, 11 are left handed.

Half the girls are left handed,

 Value D E F G
EDDIE SAYS
We already know we have 20 boys If we know that we have 11 left-handed so we must have 9 right-handed We are also told that half the girls are left-handed. If we have 12 girls, we have 6 each for left and right-handed girls
• Question 8

32 pupils are in a class. Of the 20 boys, 11 are left handed.

Half the girls are left handed,

If I pick a student at random, which of these probabilities describe picking a right handed girl?

6/32
3/16
EDDIE SAYS
This can catch people out. This question asks for a right handed girl from the class as a whole. This means the probability is 6/32. Not 6/12 The other thing that catches people is that it does not ask for it to be simplified, it asks for which ones work, so we have to click all the probabilities (simplified or not)
• Question 9

120 members of a swimming club. 56 are male.

1/4 of the female members are over 40

1/14 of the males are over 40

 Value A B C D E F G
EDDIE SAYS
We have 120 people (A) This is split into 56 males so we must have 54 females (B and C) Now it gets a bit different. We have to start dealing with fractions. 1/14 is the same as dividing by 14, so we have 4 men over 40 (D) which gives us that there are 52 men under 40 (E) 1/4 is the same as dividing by 4, so we have 16 women over 40 (F) which gives us that there are 48 women under 40 (G)
• Question 10

120 members of a swimming club. 56 are male.

1/4 of the female members are over 40

1/14 of the males are over 40

What is the probability that I pick a swimmer over 40 if I pick someone at random?

1/5
EDDIE SAYS
We can look at this and find we have 4 men over 40 and 16 women. If we have 100 in total, this initially gives a probability of 20/100. This can be cancelled down to...
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