5 PROBABILITY PROBLEM: FINITE AND INFINITE SAMPLE SPACES 1. If a national professional association is considering six hotels as possible sites for their national meeting next year, and also for the year thereafter, in how many ways can they select the hotels a. if the two consecutive national meetings are not to be held in the same hotel? b. if the two consecutive national meetings may be held in the same hotel? 2. In a research study of women who buy mutual fund shares, women interviewed were classified into seven categories of income, four categories of investment objectives, five categories of place of residence, and two categories of occupational status. In how many ways can a woman mutual fund buyer be classified? 3. An examination consists of 10 multiple-choice questions, each with 4 choices (1 of which is correct and 3 incorrect). a. In how many ways can a student mark the answer to these questions if 1 choice is made for each of the 10 questions? b. How many ways can the student get a perfect score (all correct) on this examination? c. How many ways can the student mark the answer to these questions, marking all 10 questions incorrectly? 4. If three cards are chosen from a well-shuffled deck of 52 playing cards, what are the probabilities of selecting a. 3 hearts b. No hearts c. 3 red cards d. No red cards 5. If 4 factories in a group of 24 factories in a certain community are violating environmental regulations and 6 are randomly selected for inspection, what is the probability that a. none of the violators will be selected for inspection? b. all of the violators will be selected for inspection? 65 6. Alberta, British Columbia, and Quebec are 3 of 10 provinces of Canada. Assuming that the selection is random (that each set of 3 provinces has the same chance of being selected), what are the probabilities that a marketing campaign for a new product conducted in 3 of the 10 provinces of Canada will include a. Quebec b. British Columbia and Alberta 7. The two finalists in a golf tournament play 18 holes, with the winner getting $20,000 and the runner-up getting $12,000. What are the two players mathematical expectations if a. they are evenly matched b. their probabilities of winning are and 66