1108 CHAPTER 11 Further Topics in Algebra 20. Concept Check Associate each probability in parts (a)–(e) with one of the statements in choices A–E. (a) P1E2 = 0.01 (b) P1E2 = 1 (c) P1E2 = 0.99 (d) P1E2 = 0 (e) P1E2 = 0.5 A. The event is certain. B. The event is impossible. C. The event is very likely to occur. D. The event is very unlikely to occur. E. The event is just as likely to occur as not to occur. Work each problem. See Examples 1–6. 21. Batting Average A baseball player with a batting average of .300 comes to bat. What are the odds in favor of the ball player getting a hit? 22. Small Business Loan The probability that a bank with assets greater than or equal to $30 billion will make a loan to a small business is 0.002. What are the odds against such a bank making a small business loan? 23. Drawing a Card A card is drawn at random from a standard deck of 52 cards. Find the probabilities in parts (a)–(d). (a) The card is a spade. (b) The card is not a spade. (c) The card is a spade or a heart. (d) The card is a spade or a face card. (e) What are the odds in favor of drawing a spade? 24. Dice Rolls Two fair dice are rolled. Find the probabilities in parts (a)–(d). (a) The sum of the dots is at least 10. (b) The sum of the dots is less than 10. (c) The sum of the dots is either 7 or at least 10. (d) The sum of the dots is 2, or the dice both show the same number. (e) What are the odds against rolling a 7? 25. Origins of Foreign-Born Population The numbers (in thousands) of foreign-born people who were living in the United States in 2016, according to region of birth, are given in the table. Find the probability, to the nearest thousandth, that a foreign-born U.S. resident in 2016 satisfied the following in parts (a)–(c). (a) born in Latin America (b) not born in Europe (c) born in Asia or Europe (d) What are the odds that a randomly selected foreign-born U.S. resident was born in Asia? Region Number (in thousands) Asia 12,832 Europe 4523 Latin America 22,449 Other 3266 Data from U.S. Census Bureau. 26. U.S. Population by Region The U.S. resident population by region (in millions) for selected years is given in the table. Find the probability, to the nearest thousandth, that a U.S. resident selected at random satisfied the following in parts (a)–(d). (a) lived in the West in 2014 (b) lived in the Midwest in 2010 (c) lived in the Northeast or Midwest in 2014 (d) lived in the South or West in 2018 (e) What are the odds that a randomly selected U.S. resident in 2018 was not from the South? Region 2010 2014 2018 Northeast 55.4 56.0 56.1 Midwest 67.0 67.8 68.3 South 114.9 119.7 124.8 West 72.1 75.0 78.0 Data from U.S. Census Bureau.
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