1109 11.7 Basics of Probability 27. Card Game A card game requires you to pick 1 heart, 1 club, 1 diamond, and 1 spade, in that order, from the 13 cards in each suit. What is the probability of getting all four picks correct and winning? 28. Card Game Find the probability that three of the four selections in Exercise 27 are correct. 29. Male Life Table The table is an abbreviated version of the 2015 period life table used by the Office of the Chief Actuary of the Social Security Administration. (The actual table includes every age, not just every tenth age.) Theoretically, this table follows a group of 100,000 males at birth and gives the number still alive at each age. Round answers to the questions that follow to the nearest thousandth. Exact Age Number of Lives Exact Age Number of Lives 0 100,000 60 85,802 10 99,184 70 73,100 20 98,771 80 50,564 30 97,393 90 17,915 40 95,603 100 932 50 92,632 110 2 Data from Office of the Chief Actuary, Social Security Administration. (a) What is the probability that a 40-year-old man will live 30 more years? (b) What is the probability that a 40-year-old man will not live 30 more years? (c) Consider a group of five 40-year-old men. What is the probability that exactly three of them survive to age 70? (Hint: The longevities of the individual men can be considered as independent trials.) (d) Consider two 40-year-old men. What is the probability that at least one of them survives to age 70? (Hint: The complement of at least one is none.) 30. Opinion Survey The management of a firm wishes to survey the opinions of its workers, classified as follows for the purpose of an interview: 30% have worked for the company 5 or more years, 28% are female, 65% contribute to a voluntary retirement plan, and 50% of the female workers contribute to the retirement plan. Find each probability if a worker is selected at random. (a) A male worker is selected. (b) A worker is selected who has worked for the company less than 5 yr. (c) A worker is selected who contributes to the retirement plan or is female. 31. Growth in Stock Value A financial analyst has determined the possibilities (and their probabilities) for the growth in value of a certain stock during the next year. (Assume these are the only possibilities.) See the table. For instance, the probability of a 5% growth is 0.15. If you invest $10,000 in the stock, what is the probability that the stock will be worth at least $11,400 by the end of the year? Percent Growth Probability 5 0.15 8 0.20 10 0.35 14 0.20 18 0.10 32. Growth in Stock Value Refer to Exercise 31. Suppose the percents and probabilities in the table are estimates of annual growth during the next 3 yr. What is the probability that an investment of $10,000 will grow in value to at least $15,000 during the next 3 yr? (Hint: Use the formula for (annual) compound interest.)
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