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Chapter 6 Day 3 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. Son’s Class 1 2 3 4 5 Probability .48 .38 .08 .05 .01 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) Homework Solutions #7-13 7. A. 0.04 B. 0.69 8. 0.54 9. 0.67 due to cardiovascular disease or cancer 0.33 due to other causes 10. A. 0.27 B. 0.73 11. A. 0.65 B. 0.38 C. 0.62 12. A. 1 B. 0.59 C. 0.64 13. Win a large battle 0.6 probability vs. 0.512 probability of winning three small battles Multiplication as well! Look rules work for compliments 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? What is the probability of each light not failing? What is the probability of all 20 lights not failing? 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? Example (classwork) The table below shows the probabilities of selecting a given color of M&Ms: Color Probability Brown Red Yellow Blue .20 .10 .20 .30 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?