1. A life insurance company issues standard, preferred, and ultrapreferrepold policies. Of the company's policy holders of a certain age, 60% have standard policies, 30% have preferred policies, and 10% have ultrapreferred policies. A standard policy holder has a 0.01 probability of dying next year, a preferred policy holder has a 0.008 probability of dying next year, and an ultrapreferred policy holder has a 0.007 probability of dying next year. A policy holder of that age dies in the next year. What is the probability that the policy holder had a preferred policy? 2. A survey asked a group of 400 people whether or not they were doing daily exercise. There are 227 males, 111 people who do daily exercise, and 50 males do daily exercise. A person is randomly selected. What is the probability that this person: a) Is doing their daily exercise given that they are a female? b) Is a male or not doing their daily exercise? c) Is a female and doing their daily exercise? d) Is the probability of male and doing the daily exercise independent? 3. Let A and B be independent events with ()=1 4 and ()=2 3. Compute: a) () b) () c) ( ) d) () e) ( ) 4. Urn 1 contains five white balls and three red balls. Urn 2 contains four white and six red balls. An urn is selected at uniformly at random, and a ball is drawn at random from that urn. Find the probability that, if the ball selected is white, it came from urn 1. 5. A racing car driver feels that the odds are 5 to 1 that he will not win a NASCAR race, 8 to 1 that he will not come in second, and 2 to 1 that he will come in neither first nor second. Are the odds consistent? 6. A recent Pack Poll of 1,032 NCSU students found that the proportion of seniors that favor the legalization of marijuana is 0.57 and the proportion of sophomores that favor the legalization of marijuana is 0.46. a) What are the odds that a randomly selected NCSU senior favors the legalization of marijuana? b) What are the odds that a randomly selected NCSU sophomore is against the legalization of marijuana?

7. Use the survey results for the following questions. 39% have pet now and have had a pet 61% do not have a pet now 86% have had a pet 14% do not have a pet now and have never had a pet a) Find the probability that a respondent has a pet, given that the respondent has had a pet. b) Find the probability that a respondent has never had a pet, given that the respondent does not have a pet now 8. In Orange County, 51% of the adults are males. One adult is randomly selected for a survey involving credit card usage. a) Find the prior probability that the selected person is a male. b) It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration). Use this additional information to find the probability that the selected subject is a male. 9. a) Let A and B be two events. Suppose the probability that neither A or B occurs is 2/3. What is the probability that one or both occur? b) Let C and D be two events with P(C) = 0.25, P(D) = 0.45, and P(C D) = 0.1. What is P( D)? 10. Assume that the odds against a certain horse winning a race are 5 to 2. If a bettor wins $14 when the horse wins, how much should the person bet to make the game "fair"? 11. In Ms. Tanti's geography class, 60% of the students are Canadian 28% of the students are of Chinese origin 15% are Canadian and of Chinese origin. What is the chance that a student drawn at random would be: i) Canadian or of Chinese origin? ii) Neither Canadian nor of Chinese origin? iii) Of Chinese origin, but not Canadian?

12. Shannon hits the snooze bar on her alarm clock on 60% of school days. If she doesn't hit the snooze bar, there is a 90% chance that she makes it to class on time. However, if she hits the snooze bar, there is only a 70% chance that she makes it to class on time. If Shannon is late to class, what Is the probability that she did not hit the snooze button? Is the probability that she is late for class independent from her hitting the snooze button? Justify your answer. 13. A friend says he would "give his right arm" for our two tickets to an NBA playoff game. To put this on a cash basis, we propose that he pay us $220 (the actual price of the two tickets), but he will only get them if he draws a jack, queen or king from a standard deck of playing cards; otherwise, we keep the tickets and his $220. What are the two tickets worth to our friend if he feels that this arrangement is fair? 14. A slick-talking bookie comments that since the odds against Jacksonville are 100 to 1 and the odds against Atlanta are 25 to 1, the chances of Jacksonville not winning are 4 times greater since 100= 254. Is he correct? Justify your answer.