186 CHAPTER 4 Probability Statistical Literacy and Critical Thinking 1. Notation What does the symbol ! represent? The five starting players of an NBA basketball team can stand in a line 5! different ways, so what is the actual number of ways that the five players can stand in a line? 2.Delaware Multi-Win Lotto In the Delaware Multi-Win Lotto game, a bettor selects six different numbers, each between 1 and 35. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. Do calculations for winning this lottery involve permutations or combinations? Why? 3.Delaware Play 3 In the Delaware Play 3 lottery game, a bettor selects three numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order. Do calculations for this lottery involve the combinations rule or either of the two permutation rules presented in this section? Why or why not? If not, what rule does apply? 4.Combination Lock The typical combination lock uses three numbers, each between 0 and 49. Opening the lock requires entry of the three numbers in the correct order. Is the name “combination” lock appropriate? Why or why not? In Exercises 5–36, express all probabilities as fractions. 5.Pin Numbers Use of ATM cards and hotel safes typically requires a four-digit (each 0 through 9) code, such as 3312. Digits can be repeated, but they must be entered in the correct order. If someone gains access and enters a code that was randomly selected, what is the probability of getting the correct code on the first try? 6.Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt? 7. Quinela In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 144th running of the Kentucky Derby had a field of 20 horses. What is the probability of winning a quinela bet if you randomly select the horses? 8.Soccer Shootout In the FIFA Women’s World Cup 2019, a tie at the end of two overtime periods leads to a “shootout” with five kicks taken by each team from the penalty mark. Each kick must be taken by a different player. How many ways can 5 players be selected from the 11 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth? 9.Statistics Counts How many different ways can the letters of “statistics” be arranged? If the letters of “statistics” are arranged in a random order, what is the probability that the result will be “statistics”? 10.Radio Station Call Letters Radio and Television station call letters must begin with either K (for stations west of the Mississippi River) or W (for stations east of the Mississippi River) and must include either two or three additional letters. How many different possibilities are there? 11.Scheduling Routes A presidential candidate plans to begin her campaign by visiting the capitals of 4 of the 50 states. If the four capitals are randomly selected without replacement, what is the probability that the route is Sacramento, Juneau, Hartford, and Bismarck, in that order? 4-4 Basic Skills and Concepts
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