Sets and Venn diagrams

Magda carried out a survey to find out the drinks that people like. She asked 100 people if they like coffee (C) or tea (T) or hot chocolate (H). 32 people like all three drinks. 15 people like coffee and hot chocolate but not tea. 43 people like coffee and tea. 39 people like tea and hot chocolate. 67 people like coffee. 58 people like hot chocolate. 5 people like only tea.

Complete the Venn diagram for this information.

One of the people is chosen at random. Given that this person likes coffee,

find the probability that this person also likes hot chocolate.

500 people were asked what type of film they liked best. 280 of the 500 people were adults. 100 of the adults said they liked action films best. 80 of the children said they liked thriller films best. 150 of the people said they liked action films best. 200 of the people said they liked comedy films best.

Complete the two-way table.

One of these 500 people is chosen at random.

Find the probability that this person is an adult who said they liked action films best.

E = {odd numbers between 0 and 20} A = {3, 9, 15, 17} B = {5, 7, 11, 13, 17, 19} Tom was asked to draw a Venn diagram for this information. Here is his answer.

Write down two things Tom should do to make his answer fully correct.

E = {odd numbers between 0 and 20} A = {3, 9, 15, 17} B = {5, 7, 11, 13, 17, 19} Tom was asked to draw a Venn diagram for this information. Here is his answer.

Write down two things Tom should do to make his answer fully correct.

Here is a Venn diagram.

Write down the numbers that are in set P′

A number is chosen at random from the universal set,E

Find the probability that this number is in the set P Q

Here is a Venn diagram.

Write down the numbers that are in set P′

A number is chosen at random from the universal set,E

Find the probability that this number is in the set P Q

160 people were asked to choose their favourite type of book. They each chose from romance or adventure or horror or thriller. 85 of these people were children. The rest were adults. 19 of the 33 people who chose romance were children. 34 of the 76 people who chose adventure were adults. 7 adults chose thriller. The number of children who chose thriller was the same as the number of adults who chose horror. Work out the total number of people who chose horror. You must show how you get your answer.

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {odd numbers} B = {square numbers}

Complete the Venn diagram for this information.

A number is chosen at random from the universal setE

Find the probability that this number is in the set B′

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {odd numbers} B = {square numbers}

Complete the Venn diagram for this information.

A number is chosen at random from the universal setE

Find the probability that this number is in the set B′

A shop manager wants to advertise special offers on social media platforms. The manager asks 100 customers which of type A, type B or type C they use. Of these customers, 4 use all three types 16 do not use any of type A, type B or type C 8 use both type A and type B, but not type C 14 use both type B and type C 62 in total use type A all 20 who use type C also use at least one of type A and type B.

Complete the Venn diagram for this information.

One of the customers is chosen at random. Given that this customer uses type A,

find the probability that this customer also uses type B.

E = {even numbers less than 19} A = {6, 12, 18} B = {2, 6, 14, 18} Complete the Venn diagram for this information.

E = {even numbers less than 19} A = {6, 12, 18} B = {2, 6, 14, 18} Complete the Venn diagram for this information.

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {even numbers} B = {factors of 10}

Complete the Venn diagram for this information.

A number is chosen at random from the universal set, E

Find the probability that this number is in the set A B

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {even numbers} B = {factors of 10}

Complete the Venn diagram for this information.

A number is chosen at random from the universal set, E

Find the probability that this number is in the set A B

A = {multiples of 3} B = {even numbers}

Complete the Venn diagram for this information.

E {1, 2, 3, 4, 5, 6, 7, 8, 9} A {1, 5, 6, 8, 9} B {2, 6, 9}

Complete the Venn diagram to represent this information.

A number is chosen at random from the universal set E.

Find the probability that the number is in the set A B

E {1, 2, 3, 4, 5, 6, 7, 8, 9} A {1, 5, 6, 8, 9} B {2, 6, 9}

Complete the Venn diagram to represent this information.

A number is chosen at random from the universal set E.

Find the probability that the number is in the set A B

E = {even numbers between 1 and 25} A = {2, 8, 10, 14} B = {6, 8, 20} C = {8, 18, 20, 22}

Complete the Venn diagram for this information.

A number is chosen at random from E.

Find the probability that the number is a member of A B.

E = {even numbers between 1 and 25} A = {2, 8, 10, 14} B = {6, 8, 20} C = {8, 18, 20, 22}

Complete the Venn diagram for this information.

A number is chosen at random from E.

Find the probability that the number is a member of A B.

A = {multiples of 5 between 14 and 26}

B = {odd numbers between 14 and 26}

List the members of A B

Describe the members of A B

50 people were asked if they speak French or German or Spanish.

Of these people, 31 speak French 2 speak French, German and Spanish 4 speak French and Spanish but not German 7 speak German and Spanish 8 do not speak any of the languages all 10 people who speak German speak at least one other language

Two of the 50 people are chosen at random.

Work out the probability that they both only speak Spanish.

Emma has 45 rabbits.

30 of the rabbits are male. 8 of the female rabbits have short hair. 12 of the rabbits with long hair are male.

Use the information to complete the two-way table.

One of Emma’s rabbits is chosen at random.

Write down the probability that this rabbit is a female with short hair.

E = {odd numbers less than 30} A = {3, 9, 15, 21, 27} B = {5, 15, 25}

Complete the Venn diagram to represent this information.

A number is chosen at random from the universal set, E.

What is the probability that the number is in the set A B?

E = {odd numbers less than 30} A = {3, 9, 15, 21, 27} B = {5, 15, 25}

Complete the Venn diagram to represent this information.

A number is chosen at random from the universal set, E.

What is the probability that the number is in the set A B?