 # Use Venn Diagrams for Probability

In this worksheet, students use Venn diagrams to sort data and find simple probabilities. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Combined Events and Probability Diagrams

Difficulty level:   ### QUESTION 1 of 10

A Venn diagram is something you will have probably seen before. It's two circles that crossover in the middle.

They look something like this. How and why?

This does look a bit complicated to start with until you dig down what it all means.

A set is just a list of data, be it numbers, colours or something else. So Set A and Set B are just a couple of lists.

B is the things that are in both lists.

A is what is in set A but not Set B

C is what is in set B but not in setA

D are the things that aren't in either.

Example: In a class of 30 students, 5 are in the chess club and 7 are in the debating club. There are 2 students who are in both.

Draw a Venn diagram to illustrate this. - Set A is the chess club, set B is the debating club

- We know there are 2 students in both, so B = 2

- We know there are 5 in the chess club abd that 2 are also in the debating club. This means A = 3

- We know there are 7 in the debating club but that 2 of them are also in the chess club. This means that C = 5

- So far, we have A = 3, B = 2 and C = 5. This accounts for 10 of the 30 students. This means D = 20

We can now create our Venn diagram. Example 2: A student is picked at random, what is the chance he is in the chess club and the debating club.

There are only two students that work here, this gives our probability as 2/30 which equals 1/15

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

For the Venn Diagram shown, which numbers would go in A, B, C and D Input your numbers in ascending order with a space between each one.

(For example - If you think 3, 5 and 17 need to go in D, you would enter 3 5 17)

 Which numbers would go in... A B C D

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is both a multiple of 2 and a factor of 20?

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is either a multiple of 2 or a factor of 20?

3/5

4/5

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is neither a multiple of 2 or a factor of 20?

2/5

3/5

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is either a multiple of 2 or a factor of 20 but not both?

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

Complete the Venn Diagram For each of A,B.C and D, put the amount of students who satisfy the condition.

 How many students study... A B C D

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study only Spanish

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study both Spanish and French

3/13

11/13

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study both Spanish and French

3/13

11/13

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study neither language

• Question 1

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

For the Venn Diagram shown, which numbers would go in A, B, C and D Input your numbers in ascending order with a space between each one.

(For example - If you think 3, 5 and 17 need to go in D, you would enter 3 5 17)

 Which numbers would go in... A B C D
EDDIE SAYS
This one takes a bot more thought. Set A is the factors of 20 so set A = {1,2,4,5,10,20} Set B is the multiples of 2 so Set B = {2,4,6,8,10,12,14,16,18,20} The first one we need to look at is what is in both sets. These are 2, 4, 10 and 20 (These go in B) We then look at what is in set A but not in set B. These are 1 and 5 (These go in A) Now, look at the numbers that are in set B but not in set A. These are 6, 8, 12, 14, 16 and 18 (These go in C) Our final step is to say what goes in the box. The numbers we haven\'t yet touched (from our initial numbers up to 20) are 3, 7, 9, 11, 13, 15, 17 and 19. (These go in D)
• Question 2

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is both a multiple of 2 and a factor of 20?

1/5
EDDIE SAYS
This is a bit easier now we have the Venn diagram. We have four numbers that satisfy the condition. There are 20 numbers in total. This gives a probability of 4/20 which cancels down to...
• Question 3

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is either a multiple of 2 or a factor of 20?

3/5
EDDIE SAYS
Be careful with the language here We are looking for the numbers that satisfy either condition, we don't count the numbers in the middle twice! We have twelve numbers that satisfy the condition. There are 20 numbers in total. This gives a probability of 12/20 which cancels down to...
• Question 4

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is neither a multiple of 2 or a factor of 20?

2/5
EDDIE SAYS
Be careful with the language here again We are looking for the numbers that satisfy neither condition, we only count the numbers that aren't in either circle We have eight numbers that satisfy the condition. There are 20 numbers in total. This gives a probability of 8/20 which cancels down to...
• Question 5

For all the numbers from 1 - 20

Set A is the factors of 20

Set B is the multiple of 2

This gives the Venn diagram... If I select a number at random, what is the probability is is either a multiple of 2 or a factor of 20 but not both?

2/5
EDDIE SAYS
Be careful with the language here again We are looking for the numbers that satisfy only one of the conditions, we don't count the ones in the middle. We have eight numbers that satisfy the condition. There are 20 numbers in total. This gives a probability of 8/20 which cancels down to...
• Question 6

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

Complete the Venn Diagram For each of A,B.C and D, put the amount of students who satisfy the condition.

 How many students study... A B C D
EDDIE SAYS
The first one we need to look at is what is in both sets. There are 6 students (These go in B) We then look at what is in set A but not in set B. There are 16 that study Spanish but 6 study both. There are 10 that only study Spanish (These go in A) Now, look at what is in iet B but not in set A. There are 12 that study French but 6 study both. There are 6 that only study French (These go in A) Our final step is to say what goes in the box. We have 10 that only do Spanish, 6 that do French and 6 that do bot. This leaves 4 students.
• Question 7

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study only Spanish

5/13
EDDIE SAYS
This is a bit easier now we have the Venn diagram. We have 10 students who only study Spanish There are 26 students in total. This gives a probability of 10/26 which cancels down to...
• Question 8

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study both Spanish and French

3/13
EDDIE SAYS
The common mistake with this question is to count all the people who study French and Spanish, but we're looking for the ones who do both. We have 6 students who study both There are 26 students in total. This gives a probability of 6/26 which cancels down to...
• Question 9

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study both Spanish and French

3/13
EDDIE SAYS
The common mistake with this question is to count all the people who study French and Spanish, but we\'re looking for the ones who do both. We have 6 students who study both There are 26 students in total. This gives a probability of 6/26 which cancels down to...
• Question 10

26 students are in a class, 16 study Spanish, 12 study French and six study both.

If Set A is Spanish and Set B is French

This gives the Venn diagram... If I select a student at random, what is the probability the study neither language

2/13
EDDIE SAYS
A nice easy one to finish with here We have 4 students who don't study either language. There are 26 students in total. This gives a probability of 4/26 which cancels down to...
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