188 CHAPTER 4 Probability 23. Corporate Officers and Committees The Self Driving Unicycle Company was recently successfully funded via Kickstarter and must now appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO), and chief human resources officer (CHR). It must also appoint a strategic planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee. a. How many different ways can the five officers be appointed? b. How many different ways can a committee of five be appointed? c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates? 24. ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first. a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly? b. What is the probability of randomly selecting the card’s position and finding that it is incorrectly inserted on the first attempt, but it is correctly inserted on the second attempt? (Assume that the same position used for the first attempt could also be used for the second attempt.) c. How many random selections are required to be absolutely sure that the card works because it is inserted correctly? 25. Is the Researcher Cheating? You become suspicious when a genetics researcher “randomly” selects numerous groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher claims that it is common to get 10 girls and 10 boys in such cases. a. If 20 newborn babies are randomly selected, how many different gender sequences are possible? b. How many different ways can 10 girls and 10 boys be arranged in sequence? c. What is the probability of getting 10 girls and 10 boys when 20 babies are born? d. Based on the preceding results, do you agree with the researcher’s explanation that it is common to get 10 girls and 10 boys when 20 babies are randomly selected? 26. Identity Theft with Credit Cards Credit card numbers typically have 16 digits, but not all of them are random. a. What is the probability of randomly generating 16 digits and getting your MasterCard number? b. Receipts often show the last four digits of a credit card number. If only those last four digits are known, what is the probability of randomly generating the other digits of your MasterCard number? c. Discover cards begin with the digits 6011. If you know that the first four digits are 6011 and you also know the last four digits of a Discover card, what is the probability of randomly generating the other digits and getting all of them correct? Is this something to worry about? 27. What a Word! One of the longest words in standard statistics terminology is “homoscedasticity.” How many ways can the letters in that word be arranged? 28. Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available. a. If the subjects are selected and treated one at a time in sequence, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available?
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