1. Unit 1 – Lesson A Introduction to Venn Diagrams D. Otap – Fall 2015

2. Venn Diagrams O A tool used to display how a sample or population is distributed among 2 or more characteristics

3. We want to look at how many students in have at least 1 sister and/or have at least 1 brother.

4. Let’s Create a Venn Diagram Step 1. Draw the Universal Set

5. Universal Set O Is the set of all elements under consideration O What is U for our example? O All of the students in class today

6. Step 2. Draw a circle for each possible outcome – they should overlap (We have 2 possible outcomes.) SisterBrother

7. Step 3. Notice the overlap? That section represents students who have at least 1 brother and at least 1 sister. SisterBrother

8. Step 4. What does the blue section represent? SisterBrother

9. Step 5. Determine what each section of the Venn diagram represents SisterBrother A B D C

10. OAOA Students with at least 1 sister, but no brothers OBOB Students with at least 1 sister and at least 1 brother OCOC Students with at least 1 brother, but no sisters ODOD Students who are an only child (no brothers and no sisters)

11. Complete Question 1 in Notes

12. Probability from a Venn Diagram Consider this Example SisterBrother 5 3 2 4

13. O Total Students = 5 + 3 + 4 + 2 = 14 O Total Students with a sister = 5 + 3 = 8 O Probability a student in this class has at least 1 sister is

14. Complete Question 2 in Notes

15. Notation

16. Notation (cont.)

17. Rewrite Questions 1 & 2 from 1.1 Notes

18. HW 1.1a & 1.2a WS’s

19. Your Turn O Use data from the 1 st day surveys to complete 3 different 2 part Venn Diagrams

20. Your Turn O Calculate probabilities from the Venn Diagrams you created