1. Stats 4 Day 6 conditional

2. Do Now Check your HW Questions??

3. Do Now #2 1. The probability of someone not owning a car in Chicago is 25%. 1. What is the probability of owning a car in Chicago? 2. Are owning a car and not owning a car disjoint? 2. The probability of owning a bike in Chicago (not necessarily commuting to work/school with a bike) is 70%. The probability of owning both a bike and a car is 52%. 1. What is the probability of owning a bike but not a car? 2. Are owning a car and owning a bike disjoint?

4. Does NOT affect the other event Independent DOES affect the other event Independence and Disjoint Mutually Exclusive P(A B)= 0 Disjoint Can occur together P(A B) = 0 YES!! NO!! YES!! NO!!

5. Example 1) probability of being a tall person and a boy 2) probability of rolling a 3 and a 4 3) probability of pulling a black and a jack from a deck of cards 4) wearing glasses and girl 5) wearing glasses and age 6) studying spanish and french Explain why the following are Disjoint and/or Independent

6. Independence If INDEPENDENT, probability won’t change But if DEPENDENT, probability is DIFFERENT for each category That is, the probability of event B is different than the probability of event B GIVEN event A If events are independent:

7. Independence with a Contingency Table

8. Making Trees Just like we made venn diagrams to help us with non-disjoint events, we make TREES with dependent events We can now find conditional probability, probability of B GIVEN A: P(B|A)

9. Example 1 1. What is the probability of owning a dog? 2. What is the probability of owning a dog if you are a man? 3. What is the probability of owning a dog if you are a woman? 4. If you are buying a dog, what is the probability the owner is a man?

10. We can now see that for dependent events: If events are independent:

11. Example 2 1. What is the probability of being stressed? 2. What is the probability of getting reflux if you are stressed? 3. What is the probability of getting reflux if you are not stressed? 4. What is the probability that you are stressed given you have reflux?

12. Example 3 Opinions on Gay Marriage 1.P(Support GM) 1.P(Support GM| Democrat) 1.P(Support GM| Republican) 1.P(Democrat| Support GM)

13. Worksheet

14. Homework Chapter 15 #8, 9, 12