2017/4/7 Section 5.6 (Part A) [43 points] 1. -/3 points A standard deck of playing cards has 52 cards, consisting of 13 "ranks" (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) of each of the 4 "suits" (hearts, diamonds, spades, clubs). In the game of poker each player is dealt a set of cards which is called the players "hand". If five cards are dealt to a poker player it is called a "5card poker hand". Pete is a poker player. He's just been dealt a 5card poker hand. Here are some possible events. A = He has 3 queens. B = He has 4 kings. C = He has a full house (a hand with three cards of one rank and two of a second rank). D = He has at least one spade. E = He has 2 jacks. Answer the following questions. Which of the following sets of events are mutually exclusive? (Select all that apply.) events A and B events A and C events B and D events A and E None of these, 5card poker hands can never have mutually exclusive events. Which of the following sets of events are independent? (Select all that apply.) events A and B events A and C events B and D events A and E None of these, 5card poker hands can never have independent events. Which of the following sets of events are neither mutually exclusive nor independent? (Select all that apply.) events A and B events A and C events B and D events A and E None of these, 5card poker hands can never have events which are neither mutually exclusive nor independent. http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 2/5 2017/4/7 Section 5.6 (Part A) [43 points] 2. -/2 points At the scene of a crime, the police have found a blood stain, a footprint, and some threads from a fabric. All are presumed to have been left by the person who committed the crime. After analyzing the evidence it is found that: The blood type is a type found in only 10% of the population. The footprint is a size 13 men's shoe and only 10% of the population wears that shoe size. Only 30% of the population owns clothing made from a fabric that matches the thread samples found at the scene. The police have a suspect who matches all of the criteria. He has the same blood type, the same shoe size, and owns clothing matching the threads found at the scene of the crime. While this is only circumstantial evidence, what is the probability that a random person would match all of these characteristics if the three characteristics are assumed to be independent of each other? (Give your answer correct to four decimal places.) 3. -/2 points Suppose that 15% of a population is redheaded, and 15% of the same population is lefthanded. If these two traits are independent of each other, what is the probability that a randomly selected person from this population would be both redheaded and lefthanded? 4. -/2 points Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get heads while the other three get tails OR he must get tails while the other three get heads. Of course, since it is possible for two men get heads and two men get tails, not all flips will result in finding an "odd man". If this occurs the salesmen would be forced to flip again. What is the probability that there is an "odd man" the first time they flip? http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 3/5 2017/4/7 Section 5.6 (Part A) [43 points] 5. -/6 points Kim and Susan are playing a tennis match where the winner must win 2 sets in order to win the match. For each set the probability that Kim wins is 0.59. The probability of Kim winning the set is not affected by who has won any previous sets. (a) What is the probability that Kim wins the match? (b) What is the probability that Kim wins the match in exactly 2 sets (i.e. only 2 sets are played and Kim is the one who ends up winning)? (c) What is the probability that 3 sets are played? 6. -/12 points Suppose that two teams called the Hogs and the Grunts are in a playoff series where the first team to win 2 games wins the series. For each game they play, the probability that the Hogs win is 0.52 and the probability the Grunts win is 0.48. (a) What is the probability that the Hogs win the series in exactly 2 games (i.e. only 2 games are required to finish the series and the Hogs are the ones that win)? (b) What is the probability that the Grunts win the series in exactly 2 games? (c) What is the probability that the Hogs win the series in exactly 3 games? (d) What is the probability that the Grunts win the series in exactly 3 games? (e) What is the probability that the Hogs win the series (i.e. the Hogs win but we don't care how many games are required)? (f) What is the probability that the Grunts win the series? http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 4/5 2017/4/7 Section 5.6 (Part A) [43 points] 7. -/16 points Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. For each game they play, the probability that the Bears win is 0.63 and the probability the Wildcats win is 0.37. (a) What is the probability that the Bears win the series in exactly 3 games (i.e. only 3 games are required to finish the series and the Bears are the ones that win)? (b) What is the probability that the Wildcats win the series in exactly 3 games? (c) What is the probability that the Bears win the series in exactly 4 games? (d) What is the probability that the Wildcats win the series in exactly 4 games? (e) What is the probability that the Bears win the series in exactly 5 games? (f) What is the probability that the Wildcats win the series in exactly 5 games? (g) What is the probability that the Bears win the series (i.e. the Bears win but we don't care how many games are required)? (h) What is the probability that the Wildcats win the series? http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 5/5 2017/4/7 Section 5.6 (Part B) [42 points] WebAssign Section 5.6 (Part B) [42 points] (Homework) Current Score : 2 / 42 Huizhi Liu MA 114, section 601, Spring 2017 Instructor: Lavon Page Due : Friday, April 7 2017 11:00 PM EDT 1. 1/9 points | Previous Answers Sue and Ann are taking the same English class and decide to study together. The probability that Sue makes an A in English is 0.48 and the probability that Ann makes an A is 0.31. The probability they both make A's is 0.26. (a) Are the events "Ann passes" and "Sue passes" independent events? no Are the events "Ann passes" and "Sue passes" mutually exclusive events? no (b) What is the probability that Sue makes an A but Ann doesn't? (c) What is the probability neither girl makes an A? (d) If Sue makes an A, what then is the conditional probability that Ann will also make an A? (e) If Ann makes an A, what then is the conditional probability that Sue will not make an A? 2. 1/7 points | Previous Answers Sue and Ann are taking the same English class but they do not study together, so whether one passes will be independent of whether the other passes. In other words, "Sue passes" and "Ann passes" are assumed to be independent events. The probability that Sue passes English is 0.8 and the probability that Ann passes English is 0.65. (a) What is the probability both girls pass English? (b) What is the probability neither girl passes English? (c) If Ann passes, what then is the conditional probability that Sue also passes? (c) Are the events "Ann passes" and "Sue passes" mutually exclusive events? no http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 1/3 2017/4/7 Section 5.6 (Part B) [42 points] 3. -/6 points Tom and Alice work independently in an attempt to solve a certain problem (i.e. whether one of them solves it does not affect the chances that the other will solve it). The probability that Tom solves the problem is 0.15 and the probability that Alice solves the problem is 0.4. (a) What is the probability that the problem will be solved by at least one person? (b) If you find out later that the problem has been solved by at least one person, what is the conditional probability that Tom solved it? 4. -/6 points A survey is being conducted in a county where 63% of the voters are Democrats and 37% are Republican. (a) What is the probability that two independently surveyed voters would both be Democrats? (b) What is the probability that both would be Republicans? (c) What is the probability that one would be a Democrat and one a Republican? 5. -/8 points (a) Suppose that A and B are independent events with P(A) = 0.3 and P(B) = 0.42. What is the probability that at least one of the two events occurs? (b) Suppose D, E, and F are independent events with P(D) = 0.25 , P(E) = 0.49, and P(F) = 0.14. What is the probability that at least one of the three events occurs? http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 2/3 2017/4/7 Section 5.6 (Part B) [42 points] 6. -/6 points Susie is looking for butterflies in an area where: 25% of the butterflies are of type A 10% of the butterflies are of type B 65% of the butterflies are of type C Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations). (a) What is the probability that the two butterflies she spots will both be type A butterflies? (b) What is the probability that the two butterflies she spots will be of the same type? (c) What is the probability that neither of the two butterflies she spots will be type C butterflies? Submitted http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 3/3 2017/4/7 Section 5.6 (Part C) [39 points] WebAssign Section 5.6 (Part C) [39 points] (Homework) Current Score : - / 39 Huizhi Liu MA 114, section 601, Spring 2017 Instructor: Lavon Page Due : Friday, April 7 2017 11:01 PM EDT 1. -/6 points In Major League Baseball, the American League Championship Series is a playoff round that determines the winner of the American League pennant. The winner of the series advances to play the winner of the National League Championship Series in baseball's championship, the World Series. The American League Championship Series is a "bestofseven series". This means that the winning team must win 4 games to win the series. Once a team wins 4 games the series ends and no additional games are played. Therefore, the series might be as short as 4 games (if one team wins the first four games) or it might be as long as 7 games. In the 2004 American League Championship Series the Boston Red Sox played the New York Yankees. The Yankees won the first three games, but the Red Sox rallied and won the last four games to win the series. This was the first time in the history of Major League baseball that a team had come from a 30 deficit to win a 7game playoff series. Scenario: Suppose Teams A and B are playing a "bestofseven" series. Assume that the games form independent trials where in each game played the probability that Team A wins is 0.54 and the probability that Team B wins is 0.46. What is the probability that, as in the 2004 American League Championship Series, one of the teams wins the first 3 games but the other team wins the series? (Give your answer correct to four decimal places.) 2. -/8 points The Reds and the Cubs are playing 3 games. In each game the probability that the Reds win is 0.55. The probability of the Reds winning is not affected by who has won any previous games. (a) What is the probability the Reds win all 3 games? (b) What is the probability the Reds win 2 and lose 1? (c) What is the probability the Cubs win 2 and lose 1? (d) What is the probability the Cubs win all 3 games? http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349089 1/5 2017/4/7 Section 5.6 (Part C) [39 points] 3. -/10 points In Major League Baseball the "postseason" refers to the elimination tournament held after the regular season has ended. The team that wins the postseason becomes the overall champion. The postseason consists of three rounds: the Division Series, the League Championship Series, and the World Series. The Division Series is held first. Each of the two leagues (the American League and the National League) have two "bestoffive" series (which means that the first team to win 3 games wins the series). The term "sweep", in this case, refers to a situation where the winning team wins the first three games and no additional games are needed. In the 2007 Major League Baseball postseason, fans came very close to seeing a sweep of all four of the first round playoff series. That year, the following matchups took place: American League * Boston Red Sox vs. Los Angeles Angels * Cleveland Indians vs. New York Yankees National League * Chicago Cubs vs. Arizona Diamondbacks * Philadelphia Phillies vs. Colorado Rockies What happened in 2007 is that the Rockies swept 3 straight from the Phillies, the Red Sox took 3 straight from the Angels, and the Diamondbacks beat the Cubs in 3 straight games. Fans of baseball watched with anticipation as the Indians won the first 2 games against the Yankees and it appeared that all 4 series would end in a 3game sweep. However, the Yankees squeezed out a win in game #3, and that broke the pattern. In the end it came down to game #3 of the final series played before the pattern was broken. The purpose of this problem is to investigate the probability of all series ending in 3game sweeps with this kind of playoff setup. Scenario: The following teams are paired up. Just as with the 2007 Division Series, each pair will play a "best 3outof5" series. Team A vs. Team B: in each game Team A has a 0.52 probability of winning Team C vs. Team D: in each game Team C has a 0.53 probability of winning Team E vs. Team F: in each game Team E has a 0.58 probability of winning Team G vs. Team H: in each game Team G has a 0.54 probability of winning Using the information above, answer the following questions. (Note: When calculating your answers, it is important not to round intermediate values too much or your final answers will be incorrect. For best results don't round any numbers to less than 6 decimal places.) (a) What is the probability that Team A beats Team B in a 3game sweep (i.e. wins 3 in a row without a loss)? What is the probability that Team B beats Team A in a 3game sweep? http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349089 2/5 2017/4/7 Section 5.6 (Part C) [39 points] What is the probability that the playoff series between Teams A and B results in a 3game sweep? (b) What is the probability that the playoff series between Teams C and D results in a 3game sweep? (c) What is the probability that all 4 of the playoff series (A vs. B, C vs. D, E vs. F, and G vs. H) all result in a 3game sweep? http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349089 3/5 2017/4/7 Section 5.6 (Part C) [39 points] 4. -/15 points Challenge Problem! This problem will put your understanding of the concepts learned in this section to the test. Detailed hints and tips are provided to help you along, but this problem will still take a good amount of time and effort on your part. Be patient and don't be discouraged if you don't "get it" right away. This problem is designed to challenge you are you up for the challenge? Scenario 1: Kathy drives down Hillsborough Street on Tuesday and Wednesday. Suppose that on any given day there is a 37% chance that she will have to stop for the stoplight at Brooks Ave. Hints and Tips Draw a tree diagram for this scenario. [Hint: Do this by branching up first to "stops on Tuesday" and "doesn't stop on Tuesday". Then from each of those branch up to "stops on Wednesday" and "doesn't stop on Wednesday". Figure out which numbers need to be inserted on each of the branches and "multiply up" to find the probabilities for each of the four outcomes.] (Note: In order to be successful with Scenarios 2 and 3 it is important to fully understand how find the Scenario 1 answers using the tree diagram described.) Use this tree to answer the following questions. (Give your answers correct to three decimal places.) (a) What is the probability that she will have to stop at the stoplight on Tuesday? (b) What is the probability that she will have to stop at the stoplight on both Tuesday and Wednesday? (c) What is the probability she has to stop for the stop light on exactly one of the two days? Scenario 2: April drives down Hillsborough Street on Thursday and Friday. Suppose you know that the probability she has to stop for the stoplight at Brooks Ave. on both days is 0.43. What is the probability that April will have to stop on any given day? Hints and Tips Again, you will need to draw a tree diagram. The overall layout of the tree will look similar to your tree for Scenario 1, however, this time you are not given enough information to place any numbers in your tree. To overcome this, we will assign a variable ("p") to be equivalent to P(stops on any given day). Place "p" in your tree in the appropriate places. Since we have set P(stops on any given day) = "p", this means that P(doesn't stop on a given day) must be equal to "1 p". Place "1 p" in your tree in the appropriate places. Using algebra, "multiply up" your branches to find the probability of each of the four outcomes (if you do this correctly each probability will be a mathematical statement with "p" in it). Now that you have your tree diagram with all the probabilities in terms of "p", look at the information that you were given. "Suppose you know that the probability she has to stop for the stoplight at Brooks Ave. on both days is 0.43." http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349089 4/5 2017/4/7 Section 5.6 (Part C) [39 points] Where would this 0.43 go in your tree? Use that information to write an algebraic equation. Solve this equation for "p". What is the probability that April will have to stop on any given day? Or, equivalently, what is the exact value of "p" in this scenario? (Give your answer correct to three decimal places.) Scenario 3: Becky drives down Hillsborough Street on Saturday and Sunday. Suppose you know that the probability she has to stop for the stoplight at Brooks Ave. on exactly one of these days is 0.47. What is the probability that Becky will have to stop on any given day? Hints and Tips Just as in Scenario 2, you are not given P(stops on any given day). Therefore, you'll need to draw a tree utilizing "p" and "1 p". Once you have your tree diagram with all the probabilities in terms of "p", look at the information that you were given. "Suppose you know that the probability she has to stop for the stoplight at Brooks Ave. on exactly one of these days is 0.47." Notice that there is more than one outcome in your tree that has Becky stopping on exactly one day. You'll need to add the probabilities of those branches together if you want to find the overall P(Becky stops on exactly one day). Use that information and your 0.47 value to write an algebraic equation. Solve this equation for "p". (Recall from previous math courses that to solve an equation of this nature you'll need to use the quadratic formula. If you've forgotten the formula simply do a Google search for "quadratic equation solver" there are lots of good, free ones out there for you to use. You have to get the equation in the right format, but once you do that you can use a solver to do all calculations.) You'll find that there are actually two correct answers to this question. This means that there are two possible values of "p" that could result in P(Becky stops at Brooks Ave. on exactly one of the two days) = 0.47. What is the probability that April will have to stop on any given day? Or, equivalently, what are the exact values of "p" in this scenario? (Give your answers correct to three decimal places.) (smaller value) (larger value) http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349089 5/5 2017/4/7 Section 5.6 (Part A) [43 points] 1. -/3 points A standard deck of playing cards has 52 cards, consisting of 13 "ranks" (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) of each of the 4 "suits" (hearts, diamonds, spades, clubs). In the game of poker each player is dealt a set of cards which is called the players "hand". If five cards are dealt to a poker player it is called a "5card poker hand". Pete is a poker player. He's just been dealt a 5card poker hand. Here are some possible events. A = He has 3 queens. B = He has 4 kings. C = He has a full house (a hand with three cards of one rank and two of a second rank). D = He has at least one spade. E = He has 2 jacks. Answer the following questions. Which of the following sets of events are mutually exclusive? (Select all that apply.) events A and B Which of the following sets of events are independent? (Select all that apply.) None of these, 5card poker hands can never have independent events. Which of the following sets of events are neither mutually exclusive nor independent? (Select all that apply.) events A and C events B and D events A and E 2. -/2 points At the scene of a crime, the police have found a blood stain, a footprint, and some threads from a fabric. All are presumed to have been left by the person who committed the crime. After analyzing the evidence it is found that: The blood type is a type found in only 10% of the population. The footprint is a size 13 men's shoe and only 10% of the population wears that shoe size. Only 30% of the population owns clothing made from a fabric that matches the thread samples found at the scene. The police have a suspect who matches all of the criteria. He has the same blood type, the same shoe size, and owns clothing matching the threads found at the scene of the crime. http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 2/5 2017/4/7 Section 5.6 (Part A) [43 points] While this is only circumstantial evidence, what is the probability that a random person would match all of these characteristics if the three characteristics are assumed to be independent of each other? (Give your answer correct to four decimal places.) 0.0030 3. -/2 points Suppose that 15% of a population is redheaded, and 15% of the same population is lefthanded. If these two traits are independent of each other, what is the probability that a randomly selected person from this population would be both redheaded and lefthanded? 0.0225 4. -/2 points Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get heads while the other three get tails OR he must get tails while the other three get heads. Of course, since it is possible for two men get heads and two men get tails, not all flips will result in finding an "odd man". If this occurs the salesmen would be forced to flip again. What is the probability that there is an "odd man" the first time they flip? 0.5 5. -/6 points Kim and Susan are playing a tennis match where the winner must win 2 sets in order to win the match. For each set the probability that Kim wins is 0.59. The probability of Kim winning the set is not affected by who has won any previous sets. (a) What is the probability that Kim wins the match? 0.6335 (b) What is the probability that Kim wins the match in exactly 2 sets (i.e. only 2 sets are played and Kim is the one who ends up winning)? 0.3481 (c) What is the probability that 3 sets are played? 04838 6. -/12 points http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 3/5 2017/4/7 Section 5.6 (Part A) [43 points] Suppose that two teams called the Hogs and the Grunts are in a playoff series where the first team to win 2 games wins the series. For each game they play, the probability that the Hogs win is 0.52 and the probability the Grunts win is 0.48. (a) What is the probability that the Hogs win the series in exactly 2 games (i.e. only 2 games are required to finish the series and the Hogs are the ones that win)? 0.2704 (b) What is the probability that the Grunts win the series in exactly 2 games? 02304 (c) What is the probability that the Hogs win the series in exactly 3 games? 02596 (d) What is the probability that the Grunts win the series in exactly 3 games? 0.2396 (e) What is the probability that the Hogs win the series (i.e. the Hogs win but we don't care how many games are required)? 0.53 (f) What is the probability that the Grunts win the series? 0.47 7. -/16 points Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. For each game they play, the probability that the Bears win is 0.63 and the probability the Wildcats win is 0.37. (a) What is the probability that the Bears win the series in exactly 3 games (i.e. only 3 games are required to finish the series and the Bears are the ones that win)? 0.2500 (b) What is the probability that the Wildcats win the series in exactly 3 games? 0.0507 (c) What is the probability that the Bears win the series in exactly 4 games? 0.2776 (d) What is the probability that the Wildcats win the series in exactly 4 games? 0.0957 http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 4/5 2017/4/7 Section 5.6 (Part A) [43 points] (e) What is the probability that the Bears win the series in exactly 5 games? 0.2054 (f) What is the probability that the Wildcats win the series in exactly 5 games? 0.1206 (g) What is the probability that the Bears win the series (i.e. the Bears win but we don't care how many games are required)? 0.733 (h) What is the probability that the Wildcats win the series? 0.267 http://www.webassign.net/web/Student/AssignmentResponses/last?dep=15349087 5/5 2017/4/7 Section 5.6 (Part B) [42 points] WebAssign Huizhi Liu Section 5.6 (Part B) [42 points] (Homework) MA 114, section 601, Spring 2017 Instructor: Lavon Page Current Score : 2 / 42 Due : Friday, April 7 2017 11:00 PM EDT 1. 1/9 points | Previous Answers Sue and Ann are taking the same English class and decide to study together. The probability that Sue makes an A in English is 0.48 and the probability that Ann makes an A is 0.31. The probability they both make A's is 0.26. (a) Are the events "Ann passes" and "Sue passes" independent events? no Are the events "Ann passes" and "Sue passes" mutually exclusive events? no (b) What is the probability that Sue makes an A but Ann doesn't? 0.4583 (c) What is the probability neither girl makes an A? 0.47 (d) If Sue makes an A, what then is the conditional probability that Ann will also make an A? 0.5417 (e) If Ann makes an A, what then is the conditional probability that Sue will not make an A? 0.1613 2. 1/7 points | Previous Answers Sue and Ann are taking the same English class but they do not study together, so whether one passes will be independent of whether the other passes. In other words, "Sue passes" and "Ann passes" are assumed to be independent events. The probability that Sue passes English is 0.8 and the probability that Ann passes English is 0.65. (a) What is the probability both girls pass English? 0.52 (b) What is the probability neither girl passes English? 0.007 (c) If Ann passes, what then is the conditional probability that Sue also passes? 0.8 no http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 1/3 2017/4/7 Section 5.6 (Part B) [42 points] (c) Are the events "Ann passes" and "Sue passes" mutually exclusive events? 3. -/6 points Tom and Alice work independently in an attempt to solve a certain problem (i.e. whether one of them solves it does not affect the chances that the other will solve it). The probability that Tom solves the problem is 0.15 and the probability that Alice solves the problem is 0.4. (a) What is the probability that the problem will be solved by at least one person? 0.49 (b) If you find out later that the problem has been solved by at least one person, what is the conditional probability that Tom solved it? 0.4 4. -/6 points A survey is being conducted in a county where 63% of the voters are Democrats and 37% are Republican. (a) What is the probability that two independently surveyed voters would both be Democrats? 0.3969 (b) What is the probability that both would be Republicans? 0.1369 (c) What is the probability that one would be a Democrat and one a Republican? 0.4662 5. -/8 points (a) Suppose that A and B are independent events with P(A) = 0.3 and P(B) = 0.42. What is the probability that at least one of the two events occurs? 0.594 (b) Suppose D, E, and F are independent events with P(D) = 0.25 , P(E) = 0.49, and P(F) = 0.14. What is the probability that at least one of the three events occurs? 0.63675 http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 2/3 2017/4/7 Section 5.6 (Part B) [42 points] 6. -/6 points Susie is looking for butterflies in an area where: 25% of the butterflies are of type A 10% of the butterflies are of type B 65% of the butterflies are of type C Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations). (a) What is the probability that the two butterflies she spots will both be type A butterflies? 0.0625 (b) What is the probability that the two butterflies she spots will be of the same type? 0.495 (c) What is the probability that neither of the two butterflies she spots will be type C butterflies? 0.1225 Submitted http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 3/3 2017/4/7 Section 5.6 (Part B) [42 points] WebAssign Huizhi Liu Section 5.6 (Part B) [42 points] (Homework) MA 114, section 601, Spring 2017 Instructor: Lavon Page Current Score : 2 / 42 Due : Friday, April 7 2017 11:00 PM EDT 1. 1/9 points | Previous Answers Sue and Ann are taking the same English class and decide to study together. The probability that Sue makes an A in English is 0.48 and the probability that Ann makes an A is 0.31. The probability they both make A's is 0.26. (a) Are the events "Ann passes" and "Sue passes" independent events? no Are the events "Ann passes" and "Sue passes" mutually exclusive events? no (b) What is the probability that Sue makes an A but Ann doesn't? 0.22 (c) What is the probability neither girl makes an A? 0.47 (d) If Sue makes an A, what then is the conditional probability that Ann will also make an A? 0.5417 (e) If Ann makes an A, what then is the conditional probability that Sue will not make an A? 0.1613 2. 1/7 points | Previous Answers Sue and Ann are taking the same English class but they do not study together, so whether one passes will be independent of whether the other passes. In other words, "Sue passes" and "Ann passes" are assumed to be independent events. The probability that Sue passes English is 0.8 and the probability that Ann passes English is 0.65. (a) What is the probability both girls pass English? 0.52 (b) What is the probability neither girl passes English? 0.07 (c) If Ann passes, what then is the conditional probability that Sue also passes? 0.8 no http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 1/3 2017/4/7 Section 5.6 (Part B) [42 points] (c) Are the events "Ann passes" and "Sue passes" mutually exclusive events? 3. -/6 points Tom and Alice work independently in an attempt to solve a certain problem (i.e. whether one of them solves it does not affect the chances that the other will solve it). The probability that Tom solves the problem is 0.15 and the probability that Alice solves the problem is 0.4. (a) What is the probability that the problem will be solved by at least one person? 0.49 (b) If you find out later that the problem has been solved by at least one person, what is the conditional probability that Tom solved it? 0.8163 4. -/6 points A survey is being conducted in a county where 63% of the voters are Democrats and 37% are Republican. (a) What is the probability that two independently surveyed voters would both be Democrats? 0.3969 (b) What is the probability that both would be Republicans? 0.1369 (c) What is the probability that one would be a Democrat and one a Republican? 0.4662 5. -/8 points (a) Suppose that A and B are independent events with P(A) = 0.3 and P(B) = 0.42. What is the probability that at least one of the two events occurs? 0.594 (b) Suppose D, E, and F are independent events with P(D) = 0.25 , P(E) = 0.49, and P(F) = 0.14. What is the probability that at least one of the three events occurs? 0.67105 http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 2/3 2017/4/7 Section 5.6 (Part B) [42 points] 6. -/6 points Susie is looking for butterflies in an area where: 25% of the butterflies are of type A 10% of the butterflies are of type B 65% of the butterflies are of type C Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations). (a) What is the probability that the two butterflies she spots will both be type A butterflies? 0.0625 (b) What is the probability that the two butterflies she spots will be of the same type? 0.495 (c) What is the probability that neither of the two butterflies she spots will be type C butterflies? 0.1225 Submitted http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 3/3 2017/4/7 Section 5.6 (Part B) [42 points] WebAssign Huizhi Liu Section 5.6 (Part B) [42 points] (Homework) MA 114, section 601, Spring 2017 Instructor: Lavon Page Current Score : 2 / 42 Due : Friday, April 7 2017 11:00 PM EDT 1. 1/9 points | Previous Answers Sue and Ann are taking the same English class and decide to study together. The probability that Sue makes an A in English is 0.48 and the probability that Ann makes an A is 0.31. The probability they both make A's is 0.26. (a) Are the events "Ann passes" and "Sue passes" independent events? no Are the events "Ann passes" and "Sue passes" mutually exclusive events? no (b) What is the probability that Sue makes an A but Ann doesn't? 0.22 (c) What is the probability neither girl makes an A? 0.47 (d) If Sue makes an A, what then is the conditional probability that Ann will also make an A? 0.5417 (e) If Ann makes an A, what then is the conditional probability that Sue will not make an A? 0.1613 2. 1/7 points | Previous Answers Sue and Ann are taking the same English class but they do not study together, so whether one passes will be independent of whether the other passes. In other words, "Sue passes" and "Ann passes" are assumed to be independent events. The probability that Sue passes English is 0.8 and the probability that Ann passes English is 0.65. (a) What is the probability both girls pass English? 0.52 (b) What is the probability neither girl passes English? 0.07 (c) If Ann passes, what then is the conditional probability that Sue also passes? 0.8 no http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 1/3 2017/4/7 Section 5.6 (Part B) [42 points] (c) Are the events "Ann passes" and "Sue passes" mutually exclusive events? 3. -/6 points Tom and Alice work independently in an attempt to solve a certain problem (i.e. whether one of them solves it does not affect the chances that the other will solve it). The probability that Tom solves the problem is 0.15 and the probability that Alice solves the problem is 0.4. (a) What is the probability that the problem will be solved by at least one person? 0.49 (b) If you find out later that the problem has been solved by at least one person, what is the conditional probability that Tom solved it? 0.8163 4. -/6 points A survey is being conducted in a county where 63% of the voters are Democrats and 37% are Republican. (a) What is the probability that two independently surveyed voters would both be Democrats? 0.3969 (b) What is the probability that both would be Republicans? 0.1369 (c) What is the probability that one would be a Democrat and one a Republican? 0.4662 5. -/8 points (a) Suppose that A and B are independent events with P(A) = 0.3 and P(B) = 0.42. What is the probability that at least one of the two events occurs? 0.594 (b) Suppose D, E, and F are independent events with P(D) = 0.25 , P(E) = 0.49, and P(F) = 0.14. What is the probability that at least one of the three events occurs? 0.67105 http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 2/3 2017/4/7 Section 5.6 (Part B) [42 points] 6. -/6 points Susie is looking for butterflies in an area where: 25% of the butterflies are of type A 10% of the butterflies are of type B 65% of the butterflies are of type C Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations). (a) What is the probability that the two butterflies she spots will both be type A butterflies? 0.0625 (b) What is the probability that the two butterflies she spots will be of the same type? 0.495 (c) What is the probability that neither of the two butterflies she spots will be type C butterflies? 0.1225 Submitted http://www.webassign.net/web/Student/AssignmentResponses/submit?dep=15349088 3/3