1. The choices for problem number 10, from section 6.5, in the book are given below. a. 0.4054 b. 0.1500 c. 0.5946 d. 0.7321 e. 0.2381 2. The choices for problem number 38 part d, from section 6.5, in the book are given below. a. 0.5006 b. 0.0682 C. 0.6123 d. 0.2872 e. 0.2576 3. The choices for problem number 40 part e, from section 6.5, in the book are given below. a. 0.5806 b. 0.1270 c. 0.8183 d. 0.6580 e. 0.4138 Use the following problems to answer questions 4 - 6 Of 2,000 students surveyed, 85% indicated that they commute to school each day. Of those that commute to school each day, 88% spend more than $25 a week on gasoline. Of those that do not commute to school each day, 95% indicated that they do not spend more than $25 a week on gasoline. A student surveyed is chosen at random. 4. What is the probability that this student does not commute to school each day and does not spend more than $25 a week on gas? a. 0.8075 b. 0.1425 C. 0.0500 d. 0.1200 e. 0.19005. What is the probability that this student does spend more than $25 a week on gas? a. 0.2445 b. 0.7555 C. 0.6740 d. 0.3260 e. 0.4532 6. What is the probability that this student does spend more than $25 a week on gas, given that they commute to school each day? a. 0.1200 b. 0.8300 c. 0.0500 d. 0.9500 e. 0.8800 Use the following problems to answer question 7 and 8. There are 300 seniors in Jefferson High School, of which 140 are males. It is known that 70% of the males and 65% of the females have their driver's license. If a student is selected at random from this senior class, what is the probability that the student is: 7. A female and has a driver's license? a. 0.6500 b. 0.3733 c. 0.3467 d. 0.2478 e. 0.5863 8. That they do not have a driver's license? a. 0.5234 b. 0.3267 C. 0.4286 d. 0.3497 e. 0.6108 9. The choices for problem number 12, from section 6.6, in the book are given below. a. 0.2908 b. 0.0304 c. 0.4137 d. 0.0840 e. 0.1403 10. The choices for problem number 16 part d, from section 6.6, in the book are given below. a. 0.5332 b. 0.4406 C. 0.5278 d. 0.3863 e. 0.466111. The choices for problem number 24 part b, from section 6.6, in the book are given below. a. 0.8802 b. 0.9066 C. 0.3415 d. 0.0934 e. 0.6685 Use the following problem to answer questions 12 and 13. Um 1 contains 14 green and 15 yellow marbles. Um 2 contains 11 green and & yellow marbles. An experiment consists of choosing one of two urns at random then drawing a marble from the chosen urn. Urn 1 is more likely to be chosen than Um 2 with probability 0.57. 12. What is the probability that a green marble was chosen? a. 0.5155 b. 0.3768 C. 0.4859 d. 0.5241 e. 0.4828 13. What is the probability that Urn I was chosen, if it is known that a yellow marble was drawn? a. 0.6195 b. 0.7223 C. 0.5874 d. 0.4698 e. 0.0841 Use the following problem to answer question 14. A television manufacturer has three locations where it is finally assembled. Plants A, B, and C supply 65%, 15%, and 20% respectively of the televisions used by the manufacture. Quality control has determined that 1.5% produced by Plant A are defective, while plants B and C have 2.5% defective products. 14. What is the probability that the television was manufactured by Plant B, given it was defective? a. 0.3846 b. 0.2027 c. 0.2985 d. 0.4975 e. 0.1493 15. At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 78% of landing tails. What is the probability of choosing the biased coin if you won a prize. a. 0.2146 b. 0.4084 C. 0.3421 d. 0.3056 e. 0.2670Exercise Set 6.5: Conditional Probability and Independent Events Find the following, given that P(A) =0.71, Answer the following. P(B) = 0.53, and P(An B) =0.28. 25. An experiment consists of rolling 2 dice and observing the number that lands on the 1. P(B|A) 4. P( B |A') uppermost surface. Find the probability that 2. P(A| B) 5. P(A' |B' ) the sum of the numbers is 10, given that one of the numbers is a 4. 3. P(A B ) 6. P(B' | A. ) 26. An experiment consists of rolling 2 dice and observing the number that lands on the Find the following, given that P(A) =0.56, uppermost surface. Find the probability that P(B)=0.63, and P(AnB)=0.41. the sum of the numbers is 6, given that one of the numbers is a 2. 7. P(A| B) 10. P(A B' ) 27. An experiment consists of rolling 2 dice 8. P(B|A) 11. P(B' | A. ) and observing the number that lands on the 9. P( B|A' ) 12. P(A' | B ) uppermost surface. Find the probability that the one of the numbers is a 4, given that the sum of the numbers is odd. Find the following, given that P(AUB' ) =0.82, P(AUB)" =0.24 and 28. An experiment consists of rolling 2 dice and observing the number that lands on the P(AnB')=0.33. uppermost surface. Find the probability that the one of the numbers is a 5, given that the 13. P(B| A) 16. P( B| A') sum of the numbers is even. 14. P(A| B) 17. P(A | B' ) 29. Suppose that you draw two cards from a 15. P(A B) 18. P(B' | A.) well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is an ace, Find the following, given that given that the first card is not an ace? P(AUB')=0.75, P(AUB)' =0.04, and 30. Suppose that you draw two cards from a P(AnB') =0.65. well-shuffled deck of 52 playing cards 19. P(A| B) 22. P(A B' ) without replacement. What is the probability that the second card is an ace, 20. P(B| A) 23. P(B' | A ) given that the first card is an ace? 21. P(B A.) 24. P(A' | B.) 31. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is a spade, given that the first card is not a spade? 32. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is theselected. Find the probability that: 38. An experiment consists of selecting two A. The marble is blue. marbles from an urn, in succession and B. The marble is red. without replacement. The um contains 17 C. Um 2 is chosen and a blue marble is green marbles and 16 yellow marbles. Find the probability that: drawn. D. A red marble is drawn from Um 2. A. The second marble is green. E. A red marble is drawn, given that Um 2 B. The second marble is yellow. is selected. C. Both marbles are yellow. F. A blue marble is drawn, given that Um D. Both marbles are green. I is selected. E. The second marble is green, given that the first marble is green. 36. An experiment consists of selecting an um F. The second marble is yellow, given that and then removing a marble from the urn. the first marble is green. There are & red marbles and 22 blue marbles in Ur 1, and there are 14 red 404 University of Houston Department of Mathematics Exercise Set 6.5: Conditional Probability and Independent Events 39. A survey of 1000 people was conducted A single card is drawn randomly from a and the respondents were asked if they were standard deck. Use the definition of colorblind. The results are summarized in independent events to determine if events A the following table: and B are independent. Male Female Recall: The definition of independent events Colorblind 75 23 states that events A and B are independent if Not colorblind | 411 491 and only if P(A) = P(AIB). Find the probability that: 41. Event A: Drawing a heart Event B: Drawing an Ace A. The person surveyed is colorblind. B. The person surveyed is male and 42. Event A: Drawing a King colorblind. Event B: Drawing a face card C. The person surveyed is female and not colorblind. 43. Event A: Drawing a black card D. The person is female, given that the Event B: Drawing a heart person is colorblind. E. The person is male, given that the 44. Event A: Drawing a Queen person is not colorblind. Event B: Drawing a red card 40. A survey of 1000 people was conducted 45. Event A: Drawing a diamond and the respondents were asked whether or Event B: Drawing a red card not they smoke. The results are summarized in the following table: 46. EventA: Drawing a 7 Event B: Drawing a Jack Male Female Smoker 127 A single card is drawn randomly from a Non-smoker | 403 404 standard deck. Use the product rule test to Find the probability that: determine if events A and B are independent. A. The person surveyed is a smoker. Recall: The product rule test states that B. The person surveyed is male and a non- events A and B are independent if and only if smoker. P(AnB) = P(A) -P(B). C. The person surveyed is female and a 47. Event A: Drawing a 10 smoker. Event B: Drawing an black card D. The person is female, given that the person is a non-smoker. 48. Event A: Drawing a heart E. The person is male, given that the Event B: Drawing a red card person is a smoker. 49. Event A: Drawing a face cardExercise Set 6.6: Bayes' Theorem D. A marble was selected from Urn I, if it 18. An experiment consists of selecting one of is known that the marble is green. three urns and then selecting a marble from E. The marble was selected from Ur II, if the urn. Um I contains 9 yellow marbles it is known that the marble is red and 7 brown marbles. Urn II contains 10 F. The marble is red, if it is known that the yellow marbles and 6 brown marbles. Urn marble was selected from Urn II. III contains 7 yellow marbles and 1 1 brown marbles. The probability that Urn I will be 16. An experiment consists of selecting one of selected is 0.42, the probability that Urn II two urns and then removing a marble from will be selected is 0.45, and the probability the urn. Urn I contains 19 violet marbles that Um III will be selected is 0.13. Find and 13 white marbles. Urn II contains 17 the probability that: violet marbles and 8 white marbles. A. Urn I and a yellow marble are selected. Assume that the urns are equally likely to B. A brown marble is selected. be selected. Find the probability that: C. A yellow marble is selected. A. Urn II and a white marble are selected. D. The marble was selected from Urn II, if B. A violet marble is selected. it is known that the marble is yellow. C. A white marble is selected. E. The marble was selected from Urn III, D. A marble was selected from Urn I, if it if it is known that the marble is brown. is known that the marble is violet. F. The marble is brown, if it is known that E. The marble was selected from Urn II, if the marble was selected from Urn I. it is known that the marble is white. F. The marble is white, if it is known that 19. A game consists of selecting one of three the marble was selected from Urn II. doors, opening it, and then tossing the coin that is behind the door. Door I is more 17. An experiment consists of selecting one of likely to be selected than the other two, three urns and then selecting a marble from with a probability of 0.58. The other two the urn. Urn I contains 8 blue marbles and 7 doors each have a probability of 0.21 of white marbles. Urn II contains 10 blue being selected. Behind Door I is a fair coin. marbles and 6 white marbles. Urn III Behind Door II is a biased coin with contains 7 blue marbles and 11 white probability of 0.66 that the coin lands on marbles. The probability that Urn I will be heads. Behind Door III is a biased coin, selected is 0.40, the probability that Urn II with probability of 0.28 that the coin lands will be selected is 0.30, and the probability on tails. that Urn III will be selected is 0.30. Find A. Suppose that you win a prize if the coin the probability that: lands on heads. What is the probability that you win a prize?Exercise Set 6.6: Bay' Theorem results for 6% ofpmple who do not have Celiac disease. Find the probability that: A. The blood tests show that a person does not have Celiac disease. B. The blood tests show that a person has Celiac disease. C. A person has Celiac disease and the test results were positive. D. A person has Celiac disease. given Ihat the test results were positive. E. A person does not have Celiac disease. given that the test results were positive. F. The test resulLs were negative, given that a person does not have Celiac disease. . About 3.3% of the American population has diabetes. A combination of blood tests accurately diagnoses diabetes 99.3% of the time. The tests give false positive results for l.2'll: of people who do not have the diabetes. Find the probabilin that: A. The blood tests show Ihat a person does not have diabetes. B. The blood tests show that a person has diabetes. C. A person has diabetes and the test results were positive. D. A person has diabetes. given that the Lest results were positive. E. A person does not have diabetes. given that the test results were positive. F. The test results were negative, given that a person does not have diabetes. components from Supplier B are defective and 2.3% of the components from Supplier C are defective. Find the probability that a randome selected component: A. [s defective. B. [s defective and came from Supplier B. C. [s not defective and came from Supplier C. D. [s defective. if it is known that the component came from Supplier A. E. Came from Supplier A, if it is known that the component is defective. F. Came from Supplier B. ifil is known that the component is defective. . A company buys one of its components from three different suppliers: 389E: of the components are purchased from Supplier A. 20% of the components are purchased from Supplier B. and 42% of the components are purchased from Supplier C. The company knows that some of the components will be defective: 2.4% oftl'le components from Supplier A are defective, 5.1% of the components from Supplier B are defective and L393 of the components from Supplier C are defective. Find the probability that a randome selected component: A. [s defective. B. [s defective and came from Supplier B. C. [s not defective and came from Supplier C. D. [s defective. if it is known that the component came from Supplier A. E. Came from Sunolier A. ifit is known 1. The choices for problem number 10, from section 6.5, in the book are given below. a. 0.4054 b. 0.1500 C. 0.5946 d. 0.7321 e. 0.2381 2. The choices for problem number 38 part d, from section 6.5, in the book are given below. a. 0.5006 b. 0.0682 c. 0.6123 d. 0.2872 e. 0.2576 3. The choices for problem number 40 part e, from section 6.5, in the book are given below. a. 0.5806 b. 0 c. 0.8183 d. 0.6580 e. 0.4138 Use the following problems to answer questions 4 - 6 Of 2,000 students surveyed, 85% indicated that they commute to school each day. Of those that commute to school each day, 88% spend more than $25 a week on gasoline. Of those that do not commute to school each day, 95% indicated that they do not spend more than $25 a week on gasoline. A student surveyed is chosen at random. 4. What is the probability that this student does not commute to school each day and does not spend more than $25 a week on gas? a. 0.8075 b. 0.142 c. 0.0500 d. 0.1200 e. 0.1900 5. What is the probability that this student does spend more than $25 a week on gas? 0.2445 b. 0.7555 C. 0.6740 d. 0.3260 e. 0.4532 6. What is the probability that this student does spend more than $25 a week on gas, given that they commute to school each day? a. 0.1200 b. 0.8300 c. 0.0500 d. 0.9500 e. 0.8800 Use the following problems to answer question 7 and 8. There are 300 seniors in Jefferson High School, of which 140 are males. It is known that 70% of the males and 65% of the females have their driver's license. If a student is selected at random from this senior class, what is the probability that the student is: 7. A female and has a driver's license? a. 0.6500 b. 0.373 c. 0.3467 d. 0.2478 e. 0.5863 8. That they do not have a driver's license? . 0.5234 b. 0.3267 0.4286 d. 0.3497 e. 0.6108 9. The choices for problem number 12, from section 6.6, in the book are given below. . 0.2908 b. 0.030 . 0.4137 d. 0.0840 e. 0.1403 10. The choices for problem number 16 part d, from section 6.6, in the book are given below. a. 0.5332 b. 0.440 C. 0.5278 d. 0.3863 e. 0.4661 11. The choices for problem number 24 part b, from section 6.6, in the book are given below. a. 0.8802 b. 0.9066 c. 0.3415 d. 0.0934 e. 0.6685 Use the following problem to answer questions 12 and 13. Um 1 contains 14 green and 15 yellow marbles. Urn 2 contains 11 green and 8 yellow marbles. An experiment consists of choosing one of two urns at random then drawing a marble from the chosen urn. Urn 1 is more likely to be chosen than Um 2 with probability 0.57. 12. What is the probability that a green marble was chosen? a. 0.5155 b. 0.376 c. 0.4859 d. 0.5241 e. 0.4828 13. What is the probability that Urn I was chosen, if it is known that a yellow marble was drawn? 0.6195 b. 0.7223 c. 0.5874 d. 0.4698 e. 0.0841 Use the following problem to answer question 14. A television manufacturer has three locations where it is finally assembled. Plants A, B, and C supply 65%, 15%, and 20% respectively of the televisions used by the manufacture. Quality control has determined that 1.5% produced by Plant A are defective, while plants B and C have 2.5% defective products. 14. What is the probability that the television was manufactured by Plant B, given it was defective? a. 0.3846 b. 0.2027 c. 0.2985 d. 0.4975 e. 0.1493 15. At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 78% of landing tails. What is the probability of choosing the biased coin if you won a prize. a. 0.2146 b. 0.4084 c. 0.3421 d. 0.3056 e. 0.2670Exercise Set 6.5: Conditional Probability and Independent Events Find the following, given that P(A) = 0.71, Answer the following. P(B) =0.53, and P(AnB)=0.28 25. An experiment consists of rolling 2 dice and observing the number that lands on the 1. P(B| A) 4. P( B A) uppermost surface. Find the probability that 2. P(A| B) 5. P(A B' ) the sum of the numbers is 10, given that one of the numbers is a 4. 3. P(A B) 6. P( B' | A') 26. An experiment consists of rolling 2 dice and observing the number that lands on the Find the following, given that P(A) =0.56, uppermost surface. Find the probability that P(B) =0.63, and P(AnB)=041. the sum of the numbers is 6, given that one of the numbers is a 2. 7. P(A| B) 10. P(A B ) 27. An experiment consists of rolling 2 dice 8. P(B| A) 11. P(B | A) and observing the number that lands on the 9. P(B A) 12. P(A B') uppermost surface. Find the probability that one of the numbers is a 4, given that the sum of the numbers is odd. Find the following, given that P(AUB') = 0.82, P(AUB)' = 0.24 and 28. An experiment consists of rolling 2 dice and observing the number that lands on the P(AnB') =0.33. uppermost surface. Find the probability that he of the numbers is a 5, given that the 13. P(B| A) 16. P( B A' ) sum of the numbers is even. 14. P(A| B) 17. P(A B) 29. Suppose that you draw two cards from a 15. P(A B) 18. P(B| A' ) well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is an ace, Find the following, given that given that the first card is not an ace? P(AUB') =0.75, P(AUB)' = 0.04, and P(AnB') = 0.65. 30. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards 19. P(A| B) 22. P( A| B') without replacement. What is the probability that the second card is an ace, 20. P(B| A) 23. P(B. | A') given that the first card is an ace? 21. P(B| AS ) 24. P(A B') 31. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement, What is the probability that the second card is a spade, given that the first card is not a spade? 32. Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the MATH 1324 Finite Mathematics with Applications 403 Exercise Set 6.5: Conditional Probability and Independent Events probability that the second card is red, marbles and 5 blue marbles in Ur 2. The given that the first card is red? probability that Um I is selected is 0.4 and the probability that Urn 2 is selected is 0.6. 33. An experiment consists of drawing two Find the probability that: marbles from an um and observing the color. There are 8 red marbles and 7 white A. The marble is blue. marbles in the urn. Find the probability that B. The marble is red. both marbles are red, assuming: C. A blue marble is drawn from Um 2. A. The first marble is returned to the um D. Um 2 is chosen and a red marble is before the second marble is drawn. drawn. B. The first marble is not returned to the E. A red marble is drawn, given that Um 2 urn before the second marble is drawn. is selected. F. A blue marble is drawn, given that Urn 34. An experiment consists of drawing two 1 is selected. marbles from an um and observing the color. There are 14 red marbles and 9 white 37. An experiment consists of selecting two marbles in the urn. Find the probability that marbles from an urn, in succession and both marbles are red, assuming: without replacement. The urn contains 14 green marbles and 1 1 yellow marbles. Find A. The first marble is returned to the um he probability that: before the second marble is drawn. A. The second marble is green. B. The first marble is not returned to the urn before the second marble is drawn B. The second marble is yellow C. Both marbles are yellow. 35. An experiment consists of selecting an um D. Both marbles are green. and then removing a marble from the um. E. The second marble is green, given that There are 12 red marbles and 8 blue the first marble is green. marbles in Um I, and there are 9 red marbles and 15 blue marbles in Um 2. F. The second marble is yellow, given that the first marble is green. Assume the urns are equally likely to be selected. Find the probability that: 38. An experiment consists of selecting two A. The marble is blue. marbles from an urn, in succession and B. The marble is red. without replacement. The urn contains 17 C. Um 2 is chosen and a blue marble is green marbles and 16 yellow marbles. Find drawn. the probability that: D. A red marble is drawn from Um 2. A. The second marble is green. E. A red marble is drawn, given that Urn 2 B. The second marble is yellow. is selected. C. Both marbles are yellow F. A blue marble is drawn, given that Urn D. Both marbles are green. 1 is selected. E. The second marble is green, given that the first marble is green. 36. An experiment consists of selecting an um F. The second marble is yellow, given that and then removing a marble from the urn. the first marble is green. There are 8 red marbles and 22 blue marbles in Um 1, and there are 14 red 404 University of Houston Department of Mathematics Exercise Set 6.5: Conditional Probability and Independent Events 39. A survey of 1000 people was conducted A single card is drawn randomly from a and the respondents were asked if they were standard deck. Use the definition of colorblind. The results are summarized in independent events to determine if events A the following table: and B are independent. Male Female Recall: The definition of independent events Colorblind states that events A and B are independent if Not colorblind 411 491 and only if P (A) = P(AIB). Find the probability that: 41. Event A: Drawing a heart A. The person surveyed is colorblind. Event B: Drawing an Ace B. The person surveyed is male and 42. Event A: Drawing a King colorblind. Event B: Drawing a face card C. The person surveyed is female and not colorblind. 3. Event A: Drawing a black card D. The person is female, given that the Event B: Drawing a heart person is colorblind. E. The person is male. given that the 4. Event A: Drawing a Queen person is not colorblind. Event B: Drawing a red card 10. A survey of 1000 people was conducted 5. Event A: Drawing a diamond and the respondents were asked whether or Event B: Drawing a red card not they smoke. The results are summarized in the following table: 46. Event A: Drawing a 7 Event B: Drawing a Jack Male Female Smoker 127 66 Non-smoker 403 404 card is drawn randomly from a standard deck. Use the product rule test to Find the probability that: determine if events A and B are independent. A. The person surveyed is a smoker. Recall: The product rule test states that 3. The person surveyed is male and a non- events A and B are independent if and only if smoker. P(AnB) =P(A) .P(B). C. The person surveyed is female and a 47. Event A: Drawing a 10 smoker. Event B: Drawing an black card D. The person is female, given that the person is a non-smoker. 48. Event A: Drawing a heart E. The person is male, given that the Event B: Drawing a red card person is a smoker. 19. Event A: Drawing a face card Event B: Drawing a JackExercise Set 6.6: Bayes' Theorem Use the tree diagram to find each probability Answer the following. in problems 1-6. Event D is defined to be the event that an item is defective. 13. An experiment consists of drawing two marbles from an urn in succession and na_Defective out replacement and observing the 0.027 color of the marbles. There are 14 black 0.96- marbles and 16 green marbles in the urn. Find the probability that: econd marble is green. B. The second marble is black 0.01- -0.40- C. The first marble is black, given that the Not Defective second marble is black. D. The first marble is black, given that the second marble is green. Defective E. The second marble is green, given that the first marble was black. Not Defective 14. An experiment consists of drawing two marbles from an urn in succession and 1. P(D) 2. P(D') 3. P(A|D) out replacement and observing the color of the marbles. There are 24 yellow 4. P(B D) 5. P(C D) 6. P(A D') marbles and 16 blue marbles in the um. Find the probability that: Use the tree diagram to find each probability A. The second marble is blue. in problems 7-12. Event D is defined to be the event that an item is defective. B. The second marble is yellow C. The first marble is yellow, given that the second marble is yellow. D. The first marble is yellow, given that 0.90 Not Defective the second marble is blue. E. The second marble is yellow, given that 0.28 the first marble was blue. 0.03 15. An experiment consists of selecting one of -0.31 -B 0.97- two urns and then removing a marble from O.Not Defective the um. Urn I contains 1 1 red marbles and 13 green marbles. Urn II contains 15 red marbles and 9 green marbles. Assume that 0.02-Defective the ums are equally likely to be selected. Find the probability that: Not Defective A. Um II and a green marble are selected. B. A red marble is selected. 7. P(D') 8. P(D) 9. P(B| D) C. A green marble is selected 10. P(A|D) 11. P(A D) 12. P(C | D ) Continued on the next page.. 418 University of Houston Department of Mathematics Exercise Set 6.6: Bayes' Theorem D. A marble was selected from Um I, if it 18. An experiment consists of selecting one of is known that the marble is green. three urns and then selecting a marble from The marble was selected from Urn II, if the um. Um I contains 9 yellow marbles it is known that the marble is red. and 7 brown marbles. Um II contains 10 F. The marble is red, if it is known that the yellow marbles and 6 brown marbles. Urn marble was selected from Urn II. Ill contains 7 yellow marbles and 1 1 brown marbles. The probability that Urn I will be eriment consists of selecting one of selected is 0.42, the probability that Um II two urns and then removing a marble from will be selected is 0.45, and the probability the urn. Urn I contains 19 violet marbles that Urn III will be selected is 0.13. Find and 13 white marbles. Urn II contains 17 the probability that: violet marbles and 8 white marbles. A. Um I and a yellow marble are selected. Assume that the urns are equally likely to be selected. Find the probability that: B. A brown marble is selected. C. A yellow marble is selected. A. Um II and a white marble are selected. D. The marble was selected from Um II, if B. A violet marble is selected. it is known that the marble is yellow. C. A white marble is selected. E. The marble was selected from Um II D. A marble was selected from Um I, if it if it is known that the marble is brown. nown that the marble is violet. F. The marble is brown, if it is known that E. The marble was selected from Urn II, if the marble was selected from Um I. it is known that the marble is white. marble is white, if it is known tha 19. A game consists of selecting one of three the marble was selected from Urn II. doors, opening it, and then tossing the coin hat is behind the door. Door I is more 17. An experiment consists of selecting one of likely to be selected than the other two. three urns and then selecting a marble from with a probability of 0.58. The other two the urn. Urn I contains 8 blue marbles and 7 doors each have a probability of 0.21 of white marbles. Urn II contains 10 blue ind Door I is a fair coin. marbles and 6 white marbles. Urn III is a biased coin contains 7 blue marbles and 11 white probability of 0.66 that the coin lands on marbles. The probability that Um I will be heads. Behind Door III is a biased coin, selected is 0.40, the probability that Urn II with probability of 0.28 that the coin lands will be selected is 0.30, and the probability on tails. that Um III will be selected is 0.30. Find A. Suppose that you win a prize if the coin the probability that: lands on heads. What is the probability A. Um I and a blue marble are selected. that you win a prize? B. A white marble is selecte B. If the coin lands on tails, what is the C. A blue marble is selected. probability that it was behind Door III? D. The marble was selected from Urn II, if C. If the coin lands on heads, what is the it is known that the marble is blue. probability that it was behind Door II The marble was selected from Urn III D. What is the probability that Door I is if it is known that the marble is white. selected and the coin lands on heads? F. The marble is white, if it is known that E. What is the probability that the coin the marble was selected from Um I. lands on tails, if it is known that Door II was selected? MATH 1324 Finite Mathematics with Applications 419 Exercise Set 6.6: Bayes' Theorem 20. A game consists of selecting one of three E. Plans to attend a four-year college, doors, opening it, and then tossing the coin given that the student plans to major in that is behind the door. I business likely to be selected than the other two, with a probability of 0.64. The other two F. Plans to attend a community college, given that the student plans to major in doors each have a probability of 0.18 of something other than business. being selected. Behind Door I is a fair coin. Behind Door II is a biased coin with G. Plans to major in business, given that probability of 0.75 that the coin lands on the student plans to attend a community college. heads. Behind Door III is a biased coin. with probability of 0.33 that the coin lands on tails. 22. A group of high school students were surveyed about their post-high school A. Suppose that you win a prize if the coin education plans. Of the 500 students who lands on heads. What is the probability were surveyed, 309 plan to go to a f that you win a prize? year college and 191 plan to go B. If the coin lands on tails, what is the community college. Among the students probability that it was behind Door III? who plan to attend a four-year college, 103 C. If the coin lands on heads, what is the to major in education. Among the probability that it was behind Door II? students who plan to attend a two-year D. What is the probability that Door I is college, 21 plan to major in education. Find selected and the coin lands on heads? the probability that a randomly selected surveyed student: What is the probability that the coin lands on tails, if it is known that Door II A. Plans to major in education was selected? B. Plans to major in something other than education. 21. A group of high school students were C. Plans to attend a four-year college and veyed about their post-high school major in something other than education plans. Of the 500 students education. surveyed, 371 plan to go to a four-year D. Plans to attend a community college college and 129 plan to go to a community and major in education. Among the students who plan to a four-year college, 133 plan Plans to attend a four-year college, major in business. Among the students who given that the student plans to major in plan to attend a two-year college, education. major in business. Find the probability that F. Plans to attend a community college, a randomly selected surveyed student: given that the student plans to major in something other than education. A. Plans to major in business. G. Plans to major in education, given that B. Plans to major in something other than the student plans to attend a community college. C. Plans to attend a four-year college and major in something other than business. 23. Celiac disease is present in about 0.75% of D. Plans to attend a community college the American population. A combination of and major in business. blood tests accurately diagnoses Celiac Continued in the next column... disease in people who have the disease 90% of the time. The tests give false positive University of Houston Department of Mathematics Exercise Set 6.6: Bayes' Theorem results for 6% of people who do not have components from Supplier B are defective Celiac disease. Find the probability that: and 2.3% of the components from A. The blood tests show that a person does C are defective. Find the probability that a not have Celiac disease. randomly selected component: B. The blood tests show that a person has A. Is defective. Celiac disease. B. Is defective and came from Supplier B . A person has Celiac disease and the test C. Is not defective and came from Supplier