1. Bell Ringer A manufacturing firm orders computer chips from three different companies: 9% from Company A; 23% from Company B; and 68% from Company C. Some of the computer chips that are ordered are defective: 5% of chips from Company A are defective; 3% of chips from Company B are defective; and 0.6% of chips from Company C are defective. A worker at the manufacturing firm discovers that a randomly selected computer chip is defective. What is the probability that the computer chip came from Company B? (Use a tree diagram)

2. CHAPTER 15 PART 4 “Bayes' theorem is to the theory of probability what Pythagoras’ theorem is to geometry.” ~Sir Harold Jeffreys

3. If we know P(B|A), but we need P(A|B), we can use Bayes’ Rule. However, this formula is not provided on the AP exam. We will use tree diagrams instead.

4. Example: A recent Maryland highway safety study found that in 77% of all accidents the driver was wearing a seatbelt. Accident reports indicated that 92% of those drivers escaped serious injury, but only 63% of the non-belted drivers were so fortunate. What’s the probability that a driver who was seriously injured wasn’t wearing a seatbelt? 1)Assign variables. Let B = driver wore seatbelt, NB = driver didn’t wear seatbelt Let I = serious injury, OK = no serious injury

5. Example: A recent Maryland highway safety study found that in 77% of all accidents the driver was wearing a seatbelt. Accident reports indicated that 92% of those drivers escaped serious injury, but only 63% of the non-belted drivers were so fortunate. What’s the probability that a driver who was seriously injured wasn’t wearing a seatbelt? 2) List what we know. We want to find P(NB|I). P(B) = 0.77 and P(NB) = 1 – 0.77 = 0.23 P(OK|B) = 0.92 so P(I|B) = 1 – 0.92 = 0.08 P(OK|NB) = 0.63 so P(I|NB) = 1 – 0.63 = 0.37

6. 3) Draw a tree diagram using the probabilities we listed. B NB OK I I 0.77 0.23 0.08 0.92 0.37 0.63

7. 4) Now we can calculate P(NB|I) using the original formula for conditional probability.

8. Internet addiction has been defined by researchers as a disorder characterized by spending excessive time on the Internet, impaired judgment and decision-making ability, social withdrawal, and depression. The paper “The Association between Aggressive Behavior and Internet Addiction and Online Activities in Adolescents” describes a study of a large number of adolescents. Each participant was assessed using the Chen Internet Addiction Scale to determine if he or she suffered from Internet addiction. The survey results are below: Internet Addiction (I) No Internet Addiction (NI) Total Female68450518 Male120362482 Total1888121000

9. Use the table to calculate the following: 1) P(F)3) P(I|F) 2) P(M)4) P(I|M) Now create a tree diagram for this information and then calculate: 1)P(F and I) 3) P(M and I)5) P(F|I) 2)P(F and NI)4) P(M and NI)6) P(M|I)

10. Solution : NI M I I F 0.518 0.482 0.131 0.248 0.869 0.752

11. Today’s Assignment  Add to HW: page 365 #42, 45, 46  Chapter 14 & 15 HW Due Monday  Extra Credit due Monday