Class Questions (Probability) 1. Video Games Inc. recently developed a new video game. Its market potential is to be tested by 80 veteran game players. a) What is the experiment? b) What is one possible outcome? c) Suppose 65 players tried the new game and said they liked it. Is 65 a probability? d) The probability that the new game will be a success is computed to be -1.0. Comment. e) Specify one possible event. 2. A study of 750 business administration graduates revealed 450 of the 750 were not employed in their major area of study in college. For illustration, a person who majored in accounting is now the marketing manager of an e-commerce firm. What is the probability that a particular business graduate will be employed in an area other than his or her college major? One card will be randomly selected from a standard 52-card deck. What is the probability the card will be a queen? Which approach to probability did you use to answer this question? 4. The Centre for Child Care reports on the parental status of 539 children. The parents of 333 children are married, 182 divorced, and 24 widowed. What is the probability a particular child chosen at random will have a parent who is divorced? Which approach did you use? 5. What is the probability that the S&P/TSX Composite Index will exceed 15 000 during the next 12 months? Which approach to probability did you use to answer this question? Or, Will Bishops have 2500 students in 3 years? 6. An automatic Shaw machine fills plastic bags with a mixture of beans, broccoli, and other vegetables. Most of the bags contain the correct weight, but because of the variation in the size of the beans and other vegetables, a package might be underweight or overweight. A check of 4000 packages filled in the past month revealed: Number of Probability of What is the probability that a particular package will Weight Event Packages Occurrence be either underweight or overweight? The outcome Underweight A 100 0.025 100 Satisfactory 3600 0.900 4000 "underweight" is the event A. The outcome Overweight 300 0.075 "overweight" is the event C. 4000 1.000 Use the complement rule to show the probability of a satisfactory bag. Classification # Employees Supervisors 120 Maintenance 50 Production 1460Management 302 Secretarial 53 10. 11. 12. 13. A sample of employees of Worldwide Enterprises is to be surveyed about a new pension plan. ln-depth interviews are to be conducted with each employee selected in the sample. What is the probability that the rst person selected is: i. Either in maintenance or a secretary? ii. Not in management? Draw a Venn diagram illustrating your answers to part (a). Are the events in part (a)(i) complementary or mutually exclusive or both? Routine physical examinations are conducted annually as part of a health service program for General Concrete Inc. employees. It was discovered that 8 percent of the employees need corrective shoes, 15 percent need major dental work, and 3 percent need both corrective shoes and major dental work. a) What is the probability that an employee selected at random will need either corrective shoes or major dental work? b) Show this situation in the form of a Venn diagram. What is the probability that a card chosen at random from a standard deck of cards will be either a king or a heart? A survey of the nal grades in an advanced statistics course reveals that 60 percent of the students are successful. Two students are selected at random. What is the probability that both are successful in the advanced statistics course? From experience, Teton Tire knows the probability is 0.80 that their XB-TO tire will last 100 000 km before it becomes bald or fails. An adjustment is made on any tire that does not last 100 000 km. You purchase four XB-70s. What is the probability all four tires will last at least 100 000 km? A golfer has 12 golf shirts in his closet. Suppose nine of these shirts are white and the others blue. He gets dressed in the dark, so he just grabs a shirt and puts it on. He plays golf two days in a row and does not do laundry. What is the probability that he has @ {:9 l g if? selected white shirts two days in a row? {9 i g Q i g The board of directors of Tarbell Industries consists of eight men and four women. A four-member search committee is to be chosen at random to conduct a nationwide search for a new company president. a. What is the probability all four members of the search committee will be women? b. What is the probability all four members will be men? 14. Following table provides information on Faculty rank and their ages in a university. 15. c. Does the sum of the probabilities for the events described in parts (a) and (b) equal 1? Explain. Rank Full Associate Assistant Instructor Prof. (R1) Prof. (R2) Prof. (R3) Prof. (R4) Total Under 30 (A1) 2 3 57 6 68 30-39 (A2) 52 1 70 1 63 1 7 402 40-49 (A3) 156 125 61 348 50-59 (A4) 145 68 36 4 253 60 8: over (A5) 75 15 3 93 Total 430 381 320 33 11 64 If we pick a faculty at random ; a. What is the probability of selecting an assistant professor given that he/she is 50-59 years old. A sample of executives was surveyed about loyalty to their company. One of the questions was, \"If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position\"? The responses of the executives in the survey were cross-tabulated with their length of service with the company. Among the 35 employees who had less than 1 year of service, 25 indicated that they would not remain with the company. And among the 15 employees who had 6-10 years of service, 5 indicated that they would continue with the company. Thirty employees with 1-5 years of service indicated that they would remain while 15 with the same number of service did not want to remain with the company. There were 105 employees with more than 10 years of experience. Of the total employees, 120 wanted to stay while 80 of them indicated that they would not remain with the company. 16. b. Make a contingency table. c. What is the probability of randomly selecting an executive who: d. Would remain and who has more than 10 years of service? e. Would remain or has less than one year of service? Refer to the table above a) What is the probability of selecting an executive with more than 10 years of service? b) What is the probability of selecting an executive who would not remain with the company, given that he or she has more than 10 years of service? c) What is the probability of selecting an executive with more than 10 years of service or one who would not remain with the company? Employee Retire Not Retire Total Production 5 15 20 Management 30 50 80 Total 35 65 100 18. 19. 20. A random sample of the employees of the Hardware Manufacturing Company was chosen to determine their retirement plans after age 65. Those selected in the sample were divided into management and production. a) What is the table called? b) Draw a tree diagram, and determine the joint probabilities. c) Do the joint probabilities total 1.00? Why? What is the probability that a female student will be selected at random from a class of seven males and three female students, in each of the next two class meetings? Make a tree of all possibilities. The lerum Tile and Flooring Company has two production facilities, one in Ohio and one in Virginia. The company makes the same type of tile at both facilities. The Ohio plant makes 60% of the company's total tile output and the Virginia plant 40%. All tiles from the two plants are sent to regional warehouses, where they are intermingled. After extensive study, the quality assurance manager has determined that 5% of the tiles produced in Ohio and 10% of the tiles produced in Virginia are unusable clue to quality problems. When the company sells a defective tile, it incurs not only the cost of replacing the item but also the loss of goodwill. The VP for production would like to allocate these costs fairly between the two plants. Determine the probability that a defective tile was produced by a particular production plant? There are two pharmaceutical companies Prairie and Badlands who manufacture a drug for asthma. Prairie makes 65% of the total drugs marketed and Badlands 35%. Both drugs have some side effects. 8% of the drugs made by prairie has side effects and 12% of the drugs made by awm have side effects. A drug selected has side effects, what is the probability that it came from Prairie. Prin i I f ntin . An automobile dealer wants to advertise that for $29 999 you can buy a convertible, a two-door or a four-door model, with your choice of either wire wheel covers or solid wheel covers. How many different arrangements of models and wheel covers mm mm. can the dealer offer? a . The Shopping Channel offers sweaters and slacks for women. The sweaters and slacks are offered in coordinating colours. If m a 23. 24. 25. 26. 27. sweaters are available in ve colours and the slacks are available in four colours, how many different outfits can be advertised? Pioneer manufactures three models of stereo receivers, two cassette decks, four speakers, and three CD carousels. When the four types of components are sold together, they form a \"system.\" How many different systems can the electronics rm offer? The Betts Machine Shop Inc. has eight screw machines but only three spaces available in the production area for the machines. In how many different ways can the eight machines be arranged in the three spaces available? The marketing department has been given the assignment of designing colour codes for the 42 different lines of compact disks sold by Goody Records. Three colours are to be used on each CD, but a combination of three colours used for one CD cannot be rearranged and used to identify a different CD. This means that if green, yellow, and violet were used to identify one line, then yellow, green, and violet (or any other combination of these three colours) cannot be used to identify another line. Would seven colours taken three at a time be adequate to colour code the 42 lines? A machine operator must make four safety checks before starting to machine a part. It does not matter in which order the checks are made. In how many different ways can the operator make the checks? In a lottery game, three numbers are randomly selected from a number of balls, numbered 1 though 50. a. How many permutations are possible? b. How many combinations are possible