VENN DIAGRAMS Slideshow 57, Mathematics Mr Richard Sasaki, Room 307

OBJECTIVES Review how Venn Diagrams are produced with certain types and amounts of data Review how Venn Diagrams are produced with certain types and amounts of data Be able to draw Venn Diagrams for up to three events Be able to draw Venn Diagrams for up to three events Understand how to calculate probabilities with these. Understand how to calculate probabilities with these.

VENN DIAGRAMS Venn Diagrams hold information about a certain topic. It can be about an activity, preference or an attribute. Usually, we store the information in 4 groups… Set A Set B

OR NOTATION Last lesson, we very briefly learned about OR. What is the correct notation for A or B? Set A Set B P(A) + P(B)

EXAMPLE 100 cars are examined and one is picked at random. 73 of them have air conditioning (Set A) and 31 of them have sun roofs (Set B). 10 cars have both. Draw a Venn diagram showing this. Set A Set B Calculate:

ANSWERS It doesn’t exist. People can’t mostly do both. They walk / get the bus / train etc… Set B Set A

0 mutually exclusive This means if A is true, B can’t be. Also if B is true, A can’t be. In this case… P(A) + P(B) If A is not true, does that mean B must be true?

THREE SETS Three sets gets a bit messy! You may be given lots of different information for a question. Set A Set B Set C Note: Write neatly when you draw these, otherwise you won’t be able to see what you are doing!

EXAMPLE 150 students pick their favourite 3 subjects. Students picking maths are in Set A, picking science are in Set B and social studies are in Set C. 54 students picked maths, 71 picked science and 42 picked social studies. 23 picked maths and science, 11 picked science and social studies and 8 picked maths and social studies. 4 students picked all three subjects. Set A - Maths Set B - Science Set C – Social Studies

ANSWERS - EASY Set A Set B Set C Wine A

ANSWERS - HARD Set A - Cars Set B - Robots Set C – Giraffes