6. A probability that any given person in a certain population is nearsighted is 0.15. The probability that a person is color blind is 0.07. The probability that a person is both nearsighted and color blind is 0.03. a.) What is the probability that a person selected from this population is either nearsighted or color blind (or both)? b.) What is the probability that a person is suffering from neither of these two visual impairments? c.) What is the probability that a given person is nearsighted, but not color blind? d.) What is the probability that a person is colorblind given that he or she is nearsighted? e.) What is the probability that a person is nearsighted given that he or she is color blind? 7. At a certain boys' boarding school the following are all true statements: 30% of the boys are from the northeast. 25% of the boys are from the midwest 25% of the boys are from the south 20% of the boys are from the west Of the northeastern boys, 20% are in the chess club and 40% are on the debate team Of the midwestern boys, 40% are in the chess club and 30% are on the debate team Of the southern boys, 30% are in the chess club and 60% are on the debate team Of the western boys, 50% are in the chess club and 10% are on the debate team a.) If a boy is chosen from the school at random, what is the chance he is in the chess club? b.) If a boy is chosen from the school at random, what is the chance he is on the debate team? c.) If a boy is chosen from the chess club at random, what is the chance he is from the west? d.) If a boy is chosen from the debate team at random, what is the chance he is from the northeast? 8. A high school student is taking five courses and has homework in each of the subjects every day. She insists on finishing the homework for one subject before starting on the next. a.) On any given day, in how many ways can she choose in what order she will do the five homework assignments? b.) On Tuesdays, she has study hall during the last period in the afternoon, and she can finish any two of the homework assignments during study hall. In how many ways can she choose which two assignments to do (regardless of what order she does them)? 9. There are 15 jobs that need to get done and 25 people available to do them (and capable of doing any of them). You must assign each job to just one person, and you are not going to assign more than one job to any one person. In how many ways can you assign the 15 jobs? 10. You must cancel your trip if any of three different problems come up. The probability of the first problem coming up is 0.20. For the second and third problems the probabilities are 0.25 and 0.10 respectively. Assume the probabilities of the three problems are mutually independent. What is the probability you can go on your trip