1. An Introduction to Venn Diagrams Slideshow 55, MathematicsSlideshow 55, Mathematics Mr Richard Sasaki, Room 307Mr Richard Sasaki, Room 307

2. Objectives Learn and review some new notation about different events Learn and review some new notation about different events Learn how Venn diagrams hold information Learn how Venn diagrams hold information Understand how to calculate probabilities with Venn diagrams Understand how to calculate probabilities with Venn diagrams

3. Notation At times, different events’ successes have probabilities given to you. For an event A, we assume that A can happen… How do we write “the probability of event A”? P(A) How do we write “the probability of event B”? P(B) How do we write “the probability of event A and B”? A or not happen! A

4. Venn Diagram A Venn Diagram is a diagram that shows relations between sets. Set A Set B But what if values in Set A could also be in Set B?

5. Venn Diagram Let’s make a Venn diagram about you! I want you to think about something tasty. Which do you prefer, chocolate or biscuits? Or both? Or neither?! Which is Set A? Which is Set B? Set A Set B Complete the first three rows of the table.

6. Complements How do we write the probability of picking something that isn’t in Set A? P(A') P(A') = 1 – P(A) Example P(A') =

7. Answers Question 1 3227 39 2 Set ASet B Question 2 2 7 41 0 Set ASet B

8. Practice Let’s have a bit of practice to make sure that everyone is going in the right direction. Example Draw a Venn diagram representing a sample of 100 people where 79 people like sushi (Set A), 68 people like sashimi (Set B) and 48 people like both. What is the area shown? Set A but not B Set A and B Set ASet B Set B but not A Neither Set A nor B

9. Practice 4831 20 1 Set ASet B Note: The numbers should add up to 100 (the sample size). If an element is picked at random, calculate:

10. Answers - Easy 5 14 8 3 Set ASet B 13 2 23

11. Answers - Hard 26 96 42 36 Set ASet B 18 27 7 48 26 18

12. Null Sets and Universal Sets You had to answer two questions where you didn’t know the notation (I assume). The empty set with a probability of 0, we call the null set. This is denoted “ ” (phi). The set that includes everything, with a probability of 1 is the universal set. Ironically, it’s not very universal and goes by many symbols. I used “ ” (omega) which is one of the more common ones.