Sets & Venn diagrams

A and B are two events.

Match each box on the left to the correct shaded area on the Venn diagrams. One has been done for you.

The Venn diagram shows some of the numbers of items in each set.

Work out the value of x.

x =

The Venn diagram shows some of the numbers of items in each set.

Work out the value of x.

Clive owns two coffee shops, A and B. Out of 150 people

18 people use both shops

46% use shop A

Complete the Venn diagram to represent the information.

ξ = 150 people A = people who use shop A B = people who use shop B

The Venn diagram shows information about people who work in a gym.

T = people who can work as a trainer. R = people who can work in reception.

How many people can work as a trainer and in reception?

How many people can work in reception but not as a trainer?

What fraction of all the people can work as a trainer?

A school year has 78 students. 28 wear glasses. of the students who wear glasses are left-handed. 30% of the students who do not wear glasses are left-handed.

ξ = students in the school year G = wears glasses L = left-handed

Complete the Venn diagram.

A left-handed student is chosen at random.

Work out the probability that the student wears glasses.

On the Venn diagram, shade the section represented by P ∩ Q

What does (A U B) represent in P(A U B) ? Circle your answer.

A or B or both A and B

not A and not B A but not B

The Venn diagram shows information about 80 people who visited an online shop. ξ = 80 people T = people who bought trainers H = people who bought a hoodie

One person is chosen at random.

Work out the probability that they bought a hoodie.

One person who bought trainers is chosen at random.

Work out the probability that they bought a hoodie.

A box contains 36 chocolates. The chocolates are milk or dark and have hard or soft centres. of the chocolates have soft centres. There are twice as many milk chocolates as dark. 5 of the dark chocolates have soft centres.

Complete the two-way table.

One chocolate is chosen at random.

What is the probability that it is a dark chocolate with a soft centre?

What is the probability that it has a hard centre?

Which of these represents the shaded region? Circle your answer.

B A' U B A' ∩ B A'

A walking group has 210 members. One week, the group organised a walk on Wednesday and a walk on Saturday. The frequency tree shows how many members went on the walks.

Show the information on the Venn diagram.

ξ = 210 members W = members who went on the Wednesday walk S = members who went on the Saturday walk

The Venn diagram represents 100 items.

Write down P(A ∩ B)

Work out P(A')

Work out P(A U B)

Here is a Venn diagram. ξ = 60 people H = people who own a gaming headset W = people who own a smart watch

15 of the people own a smart watch. Complete the Venn diagram.

One of the 60 people is chosen at random. What is the probability that they own both a gaming headset and a smart watch?

Marek is going to buy a gaming headset that costs £35 He already has £19 He plans to save the rest in two equal amounts over the next two weeks. He uses this method to work out in pounds how much to save each week.

What is wrong with his method?

Here is some information about 120 people who visit a shop. of the people buy neither a coat nor a dress. 19 people buy a coat. 14 people buy a dress. Complete this Venn diagram to represent the information. ξ = 120 people who visit the shop C = people who buy a coat D = people who buy a dress

Here is some information about 120 people who visit a shop. of the people buy neither a coat nor a dress. 19 people buy a coat. 14 people buy a dress. Complete this Venn diagram to represent the information. ξ = 120 people who visit the shop C = people who buy a coat D = people who buy a dress

In a group of 98 students 25 study both Art and French 10 study Art but do not study French 41 study French. Joel draws this Venn diagram to represent the information. ξ = the group of 98 students A = the students who study Art F = the students who study French

Make two criticisms of his diagram.

In a group of 98 students 25 study both Art and French 10 study Art but do not study French 41 study French. Joel draws this Venn diagram to represent the information. ξ = the group of 98 students A = the students who study Art F = the students who study French

Make two criticisms of his diagram.

Circle the expression that means the probability of A and not B.

P(A' U B) P(A U B') P(A' ∩ B) P(A ∩ B')

In a game, the player going first uses crosses and the player going second uses circles. To win the game, a player must get three crosses or three circles together in a line. The line must be horizontal, vertical or diagonal.

It is Amy’s turn to put a cross on the grid. She wins if she puts a cross in B3 Write down all the other squares where she could put a cross to win the game.

Amy goes first in the next game.

Assume that she will choose a square at random. Write down the probability that she will put her first cross in square F6

In fact, Amy decides to put her first cross into a corner square. What does this mean about the probability that she will put her first cross in square F6?

Give a reason for your answer.

At a country park there is a house, a museum and a garden. The table shows the prices per person to visit the park.

One day, 480 people visit the park. 67 visit the garden only. 40% visit the house and the museum. visit the house only. The rest visit the museum only. In total, how much do the 480 people pay to visit the park? You may use the Venn diagram to help you.

At a country park there is a house, a museum and a garden. The table shows the prices per person to visit the park.

One day, 480 people visit the park. 67 visit the garden only. 40% visit the house and the museum. visit the house only. The rest visit the museum only. In total, how much do the 480 people pay to visit the park? You may use the Venn diagram to help you.

The Venn diagram shows information about 50 people who are in bands. S = singers G = guitar players

How many of the people are guitar players?

How many of the people are singers but not guitar players?

One of the people is chosen at random. Write down the probability that the person is not a singer and not a guitar player.

Here is some information about 80 people who play in bands. 12 are singers but not guitar players. 30% are neither a singer nor a guitar player. of the guitar players are also singers. Complete this Venn diagram to represent the information.

ξ = 80 people who play in bands S = singers G = guitar players

What does A U B represent in P(A U B) ? Circle your answer.

A or B or both A but not B

not A and not B A and B

When a spinner is spun, it shows Blue (B) or Green (G) or Red (R) or White (W). When a coin is tossed, it shows Heads (H) or Tails (T). The spinner is spun and the coin is tossed. Complete this list of possible outcomes.

B H

There are 135 passengers on a plane. 3 of the passengers in Business Class are flying for the first time. In total, there are 15 passengers in Business Class. of the passengers not in Business Class are flying for the first time.

In the Venn diagram, ξ = passengers on the plane B = passengers in Business Class F = passengers flying for the first time. Complete the Venn diagram.

One of the passengers is chosen at random. Write down the probability that the passenger is in Business Class.

ξ = 29 students in a class C = students who own a cat D = students who own a dog

A student is chosen at random. Circle the probability that the student owns a cat or a dog but not both.

A student who owns a dog is chosen at random. Circle the probability that the student also owns a cat.

A and B are two events. Some probabilities are shown on the Venn diagram.

Work out P(A^/ U B)

What does (A ∩ B) represent in P(A ∩ B) ? Circle your answer.

A or B or both A but not B

not A and not B A and B

What does (A ∩ B) represent in P(A ∩ B) ? Circle your answer.

A or B or both A but not B

not A and not B A and B

Which of these represents the shaded region? Circle your answer.

The Venn diagram shows some information about 150 students. ξ = 150 students C = students who study Chemistry P = students who study Physics

The probability that a Physics student, chosen at random, also studies Chemistry is One of the 150 students is chosen at random. Work out the probability that the student does not study either Chemistry or Physics.

In a group of 20 people 7 own a dog 3 own a cat 12 do not own a dog or a cat. Aidan shows this information on a Venn diagram.

Make two criticisms of his Venn diagram.

Which of these represents the shaded region? Circle your answer.

Which of these represents the shaded region? Circle your answer.

In a tennis tournament, 98 players took part in the singles only 34 players took part in the doubles only twice as many players took part in the singles as took part in the doubles. How many players took part in both the singles and the doubles? You may use the Venn diagram to help you.

A number is picked at random from the first four prime numbers. A number is picked at random from the first four square numbers. The two numbers are added to get a score.

Complete the table.

What is the probability that the score is a prime number?

A school has 86 teachers. 42 are male and 44 are female. of the male teachers have blue eyes. of the female teachers have blue eyes.

ξ = teachers in the school M = male teachers B = teachers who have blue eyes

Complete the Venn diagram.

One teacher who has blue eyes is chosen at random. Work out the probability that the teacher is male.