Exercise Set 6.2: Introduction to Probability Answer the following. Give answers in exact form (as simplified fractions, terminating decimals, or integers, as appropriate). 1. 7. A. B. C. D. E. F. G. H. Siddharth, Anthony and Megan are running for mayor of their town. Pollsters have determined that Siddharth's probability of winning is 125 , and Megan's probability of winning is 13 . If these three candidates are the only ones running, what is the probability that Anthony will win? 8. 2. 3. Bob, Han, Tom and Iris are running for staff council president. Preliminary polling has determined that the probabilities of Bob, Tom, or Iris winning are 83 , 16 , and 1 12 , respectively. Assuming that these four candidates are the only ones running, find the probability that Han will win. 4. 5. 6. Allen, Brittney and Charla are the finalists in a reality TV show. The probability that Brittney will win is 0.38, and the probability that Charla will win is 0.35. What is the probability that Allen will win? In a bean bag toss game at a carnival, contestants can win a big bear, a small bear or a consolation prize. The probability of winning a consolation prize is 0.58. The probability of winning a small bear is 0.39. What is the probability of winning a big bear? A batch of 100 batteries is tested to determine the number of defective items. The probability that fewer than 3 batteries are defective is 0.85. The probability that the number of defective batteries is from 3 to 8 is 0.09. The probability that the number of defective batteries is from 9 to 14 is 0.05. What is the probability that 15 or more batteries are defective? MATH 1313 Finite Mathematics with Applications 9. 5 2 or 3 3 or an even number number that is not a 4 9 number greater than 1 number less than 10 8 or an odd number If a fair die is tossed, find the probability that the uppermost face displays a(n): A. B. C. D. E. F. G. H. Suppose that S = {s1 , s2 , s3 } , P ( s1 ) = 0.41 , and P ( s2 ) = 0.23 . Find P ( s3 ). If a fair die is tossed, find the probability that the uppermost face displays a(n): 7 4 1 or 3 number less than 5 number greater than 0 10 or 4 6 or an odd number 1 or 2 or 3 Suppose that you draw one card from a well-shuffled deck of 52 playing cards. What is the probability that the card that you draw is a red face card? 10. Suppose that you draw one card from a well-shuffled deck of 52 playing cards. What is the probability that the card that you draw is a black 7 or a black 8? 11. Suppose that you roll 2 dice and observe the numbers showing on the uppermost surfaces of the dice. Find the probability that the sum of the numbers is 10. 12. Suppose that you roll 2 dice and observe the numbers showing on the uppermost surfaces of the dice. What is the probability that the sum of the numbers is 3? 13. Suppose that you roll 2 dice and observe the numbers showing on the uppermost surfaces of the dice. What is the probability that the sum of the numbers is more than 8? 337 Exercise Set 6.2: Introduction to Probability 14. Suppose that you 2 two dice and observe the numbers showing on the uppermost surfaces of the dice. What is the probability that the sum is less than 5? 15. Suppose that an experiment consists of flipping a coin twice and observing the resulting sequence of heads and tails. Find the probability of observing: A. exactly one head B. at least one tail 16. Suppose that an experiment consists of flipping a coin 3 times and observing the resulting sequence of heads and tails. Find the probability of observing: A. exactly 3 tails B. exactly 2 tails Answer the following. Round each probability to the nearest ten-thousandth. 17. In a group of 248 business executives, 196 reported that they used smartphones in business. What is the probability that a randomly selected business executive in this group uses a smartphone in business? 18. Suppose that there are 327 members of a professional organization, of which 164 are over the age of 50. What is the probability that a randomly selected member of the organization is over the age of 50? that a randomly selected surveyed student plans to go to graduate school? 21. Suppose that there are 8 red marbles and 14 green marbles in an urn. One marble is selected at random. What is the probability that it is red? 22. Suppose that there are 23 black marbles and 31 white marbles in an urn. One marble is selected at random. What is the probability that it is black? 23. Suppose that there are 12 green marbles, 18 yellow marbles and 17 blue marbles in an urn. One marble is selected at random. What is the probability that it is yellow or blue? 24. Suppose that there are 10 white marbles, 21 black marbles and 15 purple marbles in an urn. One marble is selected at random. What is the probability that it is black or purple? Use the following probability distribution table to answer questions 25 - 28. Team Probability of Winning A 0.15 B 0.35 C 0.29 D 0.21 19. Out of 167 beverage orders at a coffee house, 89 were for hot beverages, while 78 were for cold beverages. What is the probability that a beverage order was for a cold beverage? 25. What is the probability that Team A or Team C will win? 20. A university surveyed 350 undergraduate students to determine their plans after graduation. Among the surveyed students, 211 said that they planned to attend graduate school, while 139 said that they planned to get a job. What is the probability 27. What is the probability that Team B will not win? 338 26. What is the probability that Team C or Team D will win? 28. What is the probability that Team D will not win? University of Houston Department of Mathematics Exercise Set 6.2: Introduction to Probability Use the following probability distribution table to answer questions 29 - 32. Event Probability s1 0.21 s2 0.17 s3 0.39 s4 0.23 29. Suppose that n = {s1 s2 } . Find P (n) . 30. Suppose that m = {s2 s3 s4 } . Find P (m). 31. Suppose that r = {s1 s3 s4 } . Find P ( r ) . 32. Suppose that t = {s2 s4 } . Find P ( t ) . Answer the following. Change each probability to a decimal. If the decimal is nonterminating, round to the nearest tenthousandth. 33. A group of college students was asked to choose between burgers, chicken tenders and tacos as their favorite fast food. The table below shows the results: Favorite Food Frequency Burgers 77 Chicken Tenders 31 Tacos 42 A. What is the sample space for this experiment? B. How many students were surveyed? C. Create a probability distribution table using this data. D. Suppose that E is the event that a student's favorite fast food is tacos. Find P ( E ) . MATH 1313 Finite Mathematics with Applications 34. A group of middle school students was asked which sport was their favorite one to watch on television. The table shown below gives the results: Favorite Sport Frequency Football 95 Basketball 66 Baseball 39 A. What is the sample space for this experiment? B. How many students were surveyed? C. Create a probability distribution table using this data. D. Suppose that E is the event that a student's favorite sport to watch on television is football. Find P ( E ) . 35. A group of female shoppers completed a survey which asked for shoe size. The table below gives the results: Shoe Frequency Size Shoe Frequency Size 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 3 4 2 6 12 18 25 29 35 37 31 14 9 A. What is the sample space for this experiment? B. How many women were surveyed? C. Create a probability distribution table using this data. D. Suppose that E is the event that a woman's shoe size is greater than size 7. Find P ( E ) . 339 Exercise Set 6.2: Introduction to Probability 36. A bakery tallied the number of sales of various flavors of cupcakes. The table shown gives the results: Flavor Frequency Vanilla 125 Chocolate 185 Red Velvet 54 Lemon 6 Italian Cream 12 Carrot 18 A. What is the sample space for this experiment? B. How many sales were tallied? C. Create a probability distribution table using this data. D. Suppose that E is the event that a cupcake sold was either chocolate or red velvet. Find P ( E ) . 37. Some high school seniors were surveyed regarding their scores on the ACT test. The results are given in the table shown below: 38. A car dealership surveyed some new car buyers and asked each how many miles s/he intended to drive on her/his new car before trading it in. The results are given in the table: Number of Miles Frequency Fewer than 25,000 17 25,001 - 75,000 56 75,001 - 125,000 87 125,001 - 175,000 31 175,001 or more 9 A. What is the sample space for this experiment? B. How many new car owners were surveyed? C. Create a probability distribution table using this data. D. Suppose that E is the event that a new car buyer intends to drive her/his car more than 75,000 miles. Find P ( E ) . Score range Number of students 31 - 36 46 25 - 30 94 19 - 24 147 13 - 18 156 0 - 12 57 A. What is the sample space for this experiment? B. How many students were surveyed? C. Create a probability distribution table using this data. D. Suppose that E is the event that a student's score was greater than 25. Find P ( E ) . 340 University of Houston Department of Mathematics Math 1313 Homework 18 Section 6.2 1. The choices for problem number 4 from the book are given below. a. 0.62 b. 0.73 c. 0.65 d. 0.27 e. None of the above. 2. The choices for problem number 6 from the book are given below. a. 0.99 b. 0.09 c. 1 d. 0.01 e. None of the above. 3. The choices for problem number 8 part d from the book are given below. a. 0.1667 b. 0.8333 c. 0.3333 d. 0.6667 e. None of the above. 4. The choices for problem number 14 from the book are given below. a. 0.1111 b. 0.3889 c. 0.8889 d. 0.1667 e. None of the above. 5. The choices for problem number 18 from the book are given below. a. 0.1529 b. 0.6544 c. 0.3049 d. 0.5015 e. None of the above. 6. The choices for problem number 22 from the book are given below. a. 0.0435 b. 0.0323 c. 0.0189 d. 0.0185 e. 0.4259 7. The choices for problem number 26 from the book are given below. a. 0.29 b. 0.21 c. 0.50 1 Math 1313 Homework 18 Section 6.2 d. 0.08 e. None of the above. 8. The choices for problem number 30 from the book are given below. a. 0.79 b. 0.17 c. 0.01 d. 0.21 e. None of the above. 9. The choices for problem number 36 part a from the book are given below. a. b. c. d. S = {6, 12, 18, 54, 125, 185} S = {Vanilla, Chocolate, Red Velvet, Lemon, Italian Cream, Carrot} S = {400} None of the above 10. The choices for problem number 36 part c from the book are given below a. Flavor Vanilla Chocolate Red Velvet Lemon Italian Cream Carrot Probability 0.3125 0.4625 0.135 0.15 0.3 0.45 b. Flavor Vanilla Chocolate Red Velvet Lemon Italian Cream Carrot Probability 1.25 1.85 0.54 0.06 0.12 0.18 c. Flavor Vanilla Chocolate Red Velvet Lemon Italian Cream Carrot Probability 0.3125 0.4625 0.135 0.015 0.03 0.045 d. Flavor Vanilla Chocolate Red Velvet Lemon Italian Cream Carrot Probability 0.125 0.185 0.054 0.006 0.012 0.018 e. None of the above 2