1. Chapter 6 Day 3

2. Warm-Up  A sociologist studies social mobility in England by recording the social class of a large sample of fathers and their sons. The social classes are ordered from Class 1 (lowest) to Class 5 (highest). Here are the probabilities that the son of a lower class (Class 1) father will end up in each social class.  Let A be the event that the son remains in class 1  Let B be the event that the son reaches one of the two highest classes.  Find the following probabilities  P(A)  P(B)  Probability that the son does NOT remain in class 1? P(A c )  Probability that the son remains in the lower class or reaches one of the top two classes. P(A or B) Son’s Class12345 Probability.48.38.08.05.01

3. Homework Solutions #7-13 7.A. 0.04B. 0.69 8. 0.54 9. 0.67 due to cardiovascular disease or cancer 0.33 due to other causes 10. A. 0.27B. 0.73 11. A. 0.65B. 0.38C. 0.62 12. A. 1B. 0.59C. 0.64 13. Win a large battle 0.6 probability vs. 0.512 probability of winning three small battles

4.  Multiplication rules work for compliments as well!  Look at example #15  A string of Christmas lights contains 20 lights. The lights are wired in a series, so that if any light fails the whole string will go dark. Each light has a probability or 0.02 of failing during a 3-year period. The lights fail independently of each other. What is the probability that the string of lights will remain bright for 3 years?

5.  What is the probability of each light not failing?  What is the probability of all 20 lights not failing?

6. Example  Most sample surveys use random digit dialing equipment to call residential telephone numbers at random. The telephone polling firm Zogby International reports that the probability that a call reaches a live person is 0.2. Calls are independent.  A polling firm places 5 calls. What is the probability that none of them reaches a person?  When calls are made to NYC, the probability of reaching a person is only 0.08. What is the probability that none of 5 calls made to NYC reaches a person?

7. Example (classwork)  The table below shows the probabilities of selecting a given color of M&Ms:  Does the table contain all colors? How do you know?  What is the probability of choosing and M&M of a different color than what is listed?  What is the probability of choosing an M&M that is brown or yellow?  If you choose 2 M&Ms at random, what is the probability that both are brown or yellow? Color BrownRedYellowBlue Probability.20.10.20.30