How Can I Practice? $20,000 < SALARY < $50, years. 24 More than Total. i. 12 years of education and makes more than $100,000.
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1 774 CHAPTER 6 PROBABILITY MODELS Activities How Can I Practice? 1. The following table displays the annual salaries and years of education for a cross section of the population. Complete the totals for each category. Then calculate the relative frequency for each entry. EDUCATION 12 years LESSTHAN $20, $20,000 < SALARY < $50, $50,000 < SALARY < $100, MORETHAN $100,000 4 TOTAL 14 years years More than Total a. If an individual is selected at random, use the corresponding relative frequencies to estimate the probability that the person has: i. 12 years of education and makes more than $100,000. ii. 14 years of education and makes less than $20,000. iii. more than 16 years of education and makes more than $50,000. b. Given that the individual chosen has 14 years of education, what is the probability that he or she makes more than $50,000? c. Given that the individual chosen has 16 or more years of education, what is the probability that she or he makes more than $50,000? 2. A vase contains 35 marbles: 10 blue, 8 green, 7 yellow, 5 red, and 5 white. One marble is selected at random. Find the following probabilities. a. P(red) b. P(noi blue) c. /"(green or white) d. P(black) e. f(not black) Ji
2 HOW CAN I PRACTICE? If a six-sided die is rolled four times, how many different four-digit sequences are possible? 4. If a six-sided die is rolled three times, how many branches will be in the tree that displays the sample space? 5. If a coin isflippedfour times, determine the probability distribution for the number of tails. x, THE NUMBER OF TAILS P(x) 6. A coin is flipped and a fair die is rolled. a. Construct a tree diagram showing all the possible outcomes. b. Determine the probability that a head shows and a 2 is rolled. c. What is the probability that a tail shows or an even number is rolled? 7. The school's Guidance Counselor submitted a report to the School Board summarizing the percentage of students in grades 9-12 that were studying a language other than English. The results are given in the table. SPANISH FRENCH 1 GERMAN 1 OTHER NONE 26% 9% 3% 3% 59%
3 776 CHAPTER 6 PROBABILITY MODELS Determine the probability that a randomly selected student in grades 9 12 is a. studying Spanish b. not studying French c. studying French or German 8. The land area of Canada is 9,094,000 square kilometers. Of this land, 4,176,000 square kilometers is forested. A square kilometer of land in Canada is randomly selected. a. What is the probability that the selected area of land is forested? b. What is the probability that it is not forested? 9. During World War II, the British determined that the probability that a bomber was lost through enemy action on a mission over occupied Europe was a. What is the probability that a bomber survived its mission? b. What is the probability that a bomber survived 2 missions? Assume the events are independent. c. What is the probability that a bomber returns safely after 10 missions? 10. Each of the six joints in the Challenger space shuttle's booster rocket had a reliability. The six rocket joints worked independently. a. What does it mean that the six rocket joints work independently? b. A reliability means that the probability of a rocket joint working successfully is What is the probability that all six rocket booster joints work successfully?
4 HOW CAN I PRACTICE? The following table gives the number of degrees (in thousands) earned in the United States in the academic year. BACHELOR'S MASTER'S PROFESSIONAL 1 DOCTORATE 1 TOTAL 1 Female Male Total a. Complete the table. b. If a student receiving a degree is randomly selected, what is the probability that the person selected is female? c. What is the probability that the degree recipient is a male who earned a Doctorate? d. What is the probability that the person is a female, given that the person received a Master's degree? e. What is the probability that the person selected received a bachelor's degree, given the recipient is male? f. What is the probability the person selected is a female or received a professional degree? 12. In a recent year, the percentage of computer games sold is summarized in the following table: GAMETYPE Strategy Family and Children's Shooters Role Playing Sports Other Percentage 26.9% 20.3% 16.3% 10.0% 5.4% 21.1% a. What is the probability that a computer game sold was a strategy or shooters game? b. What is the probability that the computer game is not a family game?
5 778 CHAPTER 6 PROBABILITY MODELS c. What is the probability that the computer game sold is a strategy game, given it is not a sports game? 13. If a license plate consists of three letters (excluding I and O) followed by three digits (excluding 0 and 1), how many different plates are possible? 14. You have ten books to arrange on your bookshelf. How many different orderings of all ten books are possible? 15. There are 96 boys in the freshman class. If five boys are selected at random to form a new rock band, how many possible bands are there? 16. If the band members in the previous problem are to be assigned specific instruments (drams, bass, keyboard, guitar, and vocals), how many bands are possible? 17. How many five-digit numbers are possible, if no digit can be repeated (and 0 as the first digit is allowed)? 18. If a coin is flipped 30 times, how many possible ways could there be exactly 10 heads? 19. If a fair coin is flipped 10 times, and heads comes up every time, what is the probability that on the next flip the coin will come up tails? 20. What is the probability that in a family with 12 children, exactly half of them are boys? 21. Suppose you know 2% of all switches are defective. If two switches are used in a device: a. What is the probability that both switches are good? b. What is the probability that exactly one switch is good? c. What is the probability that at least one switch is good?
6 HOW CAN I PRACTICE? 779 d. Could you also determine your answer to part c by subtracting the probability of getting two defective switches from 1? e. What is the minimum number of switches that need to be selected so the probability of getting at least one good switch is greater than ? 22. In playing Monopoly, rolling doubles three times in a row sends you to jail. a. What is the probability of rolling three consecutive doubles? b. If you roll the dice 100 times over the course of a game, what is the probability that you will have rolled doubles, at any point, exactly three times?
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