Review Exercises 181 Telephone Numbers The telephone numbers for a region of Pennsylvania have an area code of 570.The next seven digits represent the local telephone numbers for that region.These cannot begin with a 0 or 1. In Exercises 15 and 16, assume your cousin lives within the given area code. 15. What is the probability of randomly generating your cousin’s telephone number on the first try? 16. What is the probability of not randomly generating your cousin’s telephone number on the first try? Section 3.2 In Exercises 17 and 18, use the table, which shows the numbers of first-time and repeat U.S. nursing students taking the National Council Licensure Examination (NCLEX-RN® exam) to pass or fail in a recent year. (Adapted from National Council Licensure Examinations) Passed Failed Total First time 177,407 27,522 204,929 Repeat 44,983 59,775 104,758 Total 222,390 87,297 309,687 17. Find the probability that a student took the exam for the first time, given that the student failed. 18. Find the probability that a student passed, given that the student repeated the exam. In Exercises 19–22, determine whether the events are independent or dependent. Explain your reasoning. 19. Tossing a coin four times and getting four heads, and then tossing it a fifth time and getting a head 20. Selecting an ace from a standard deck of 52 playing cards, and then selecting a jack from the deck without replacing the ace 21. Taking a driver’s education course and passing the driver’s license exam 22. Getting high grades and being awarded an academic scholarship 23. Your roommate asks you to buy toothpaste and dental rinse but does not tell you which brands to get. The store has eight brands of toothpaste and five brands of dental rinse. What is the probability that you will purchase the correct brands of both products? Is this an unusual event? Explain. 24. Your sock drawer has 18 folded pairs of socks, with 8 pairs of white, 6 pairs of black, and 4 pairs of blue. What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair? Is this an unusual event? Explain. Section 3.3 In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning. 25. Event A: Randomly select a red jelly bean from a jar. Event B: Randomly select a yellow jelly bean from the jar. 26. Event A: Randomly select a person who loves cats. Event B: Randomly select a person who owns a dog.
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