Maths year 10/11: Venn diagrams, Sets {}, Unions ∪ , Intersections ∩ , Universal U

A set is a collection of things.

e.g. 2, 3, 5, 7, 11 is a set of prime numbers

and 2, 4, 6, 8, 10 is a set of even numbers

We write Sets inside curly brackets: Prime = {2, 3, 5, 7, 11}

We can also draw a picture like this:

Q: Write the set Even made from 2, 4, 6, 8, 10

ANSIf you show the numbers as Prime OR even numbers it is called a **U**nion of sets with the symbol ∪

Prime ∪ Even = {2, 3, 4, 5, 6, 7, 8, 10, 11}

Not all numbers are in this set - some odd numbers are missing.

The results can be shown in a **Venn diagram**

Q1: What information can you obtain from the Venn diagram

Q2: For the numbers 1 to 16 show Even ∪ Square numbers

ANS80 children were asked if they preferred Milk or Orange juice.

70 prefer at least one of the drinks

35 prefer milk, but not orange juice

24 prefer orange juice, but not milk

Q1: Complete the Venn diagram, writing the number of children in each part.

Q2: One of the children is picked at random. Work out P(M ∩ O).

ANSA group of pupils were asked about their liking for English and Maths.

The information is shown on the Venn diagram.

Q1: How many pupils were asked

Q2: A pupil wa selected at random

What is the probability that they like both Maths and English

Q3: Given that a pupil does not like Maths

Find the probability that they don't like English.

A set of pupils were asked which TV programs they watched.

They were given the following options: CBBC, Paw Patrol, Dr Who or None.

Here is a list of TV programs they watched:

Program | Name |

CBBC | Henry, Sue, Jess, Pops, Lou, Dave |

Paw Patrol | Stu, Jess, Dave, Jane |

Dr Who | Kath, Dave, Jane, Matt, Lou |

None | Bill |

Draw a Venn diagram to show the information.

ANSDavid asked 100 people which drink they liked from Coffee, Tea or Milk.

9 people liked all three drinks

21 people liked milk and coffee

25 people liked milk and tea

24 people liked tea and coffee

53 people liked tea

53 people liked coffee

51 people liked milk

How many people did not like tea, coffee or milk.

ANSGiven that the person selected at random from 100 people liked tea find the probability that they also liked coffee.

ANSThere are 250 pupils in Year 11 taking some, if not all, of these exams: French, History and Drama.

92 pupils are taking History and Drama but not French

96 pupils are taking French and Drama but not History

95 pupils are taking History and French but not Drama

80 pupils are taking all three exams

127 are taking Drama in total

132 are taking French in total

126 are taking History in total

How many pupils do not take any of these exams?

ANSGiven that a pupil selected at random took one of these exams find the probability that they only took Drama.

ANS