1. Unit 5 Lesson 4 Probability 6.5 Independence

2. Independent Events Two events are independent if knowing that one will occur (or has occurred) does not change the probability that the other occurs. Two events, E and F, are said to be independent if P(E|F) = P(E). If P(E|F) = P(E), it is also true that P(F|E) = P(F). If two events are not independent, they are said to be dependent events.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Testing for Independences Were “Class” and “Survival” independent variables? Did one class have more or less of a chance of surviving than another class?

4. Let ’ s consider a bank that offers different types of loans: The bank offers both adjustable-rate and fixed-rate loans on single-family dwellings, condominiums and multifamily dwellings. The following table, called a joint- probability table, displays probabilities based upon the bank ’ s long-run loaning practices. Single FamilyCondoMultifamilyTotal Adjustable.40.21.09.70 Fixed.10.09.11.30 Total.50.30.20 P(Adjustable loan) =.70

5. Bank Loan ’ s Continued... Single FamilyCondoMultifamilyTotal Adjustable.40.21.09.70 Fixed.10.09.11.30 Total.50.30.20 P(Adjustable loan) =.70 P(Adjustable loan|Condo) =.21/.30 =.70 Knowing that the loan is for a condominium does not change the probability that it is an adjustable-rate loan. Therefore, the event that a randomly selected loan is adjustable and the event that a randomly selected loan is for a condo are independent.

6. Practice with Homework Pg.267: #6.36, 6.38, 6.40, 6.41, 6.43, 6.45, 6.46, 6.48