EXERCISE 1 (CHAPTER 3) 1.For each of the following, indicate whether the type of probability involved is an example of classical probability, empirical probability or subjective probability: a) the next toss of a fair coin will land on heads. b) c) d) 2. Italy will win soccer’s World Cup the next time the competition is held. the sum of the faces of two dice will be 7. the train taking a commuter to work will be more than 10 minutes late. A test contains two multiple-choice questions. If a student makes a random guess to answer each question, how many outcomes are possible? Draw a tree diagram for this experiment. (Hint: Consider two outcomes for each question – either the answer is correct or it is wrong). Refer to question 2 above. List all the outcomes included in each of the following events and mention which are simple and which are compound events. a) Both answers are correct. b) c) d) At most one answer is wrong. The first answer is correct and the second is wrong. Exactly one answer is wrong. 3. 4. State whether the following events are independent or dependent. a) Getting a raise in salary and purchasing a new car. b) c) d) Having a large shoe size and having a high IQ. A father being left-handed and a daughter being left-handed. Eating an excessive amount of ice cream and smoking an excessive amount of cigarettes. 5. 88% of American children are covered by some type of health insurance. If four children are selected at random, what is the probability that none are covered? (0.0002) A box of nine golf gloves contains two left-handed gloves and seven right-handed gloves. a) If two gloves are randomly selected from the box without replacement, what is the probability that both gloves selected will be right-handed? (0.5833) b) If three gloves are randomly selected from the box without replacement, what is the probability that all three will be left-handed? (0) c) If three gloves are randomly selected from the box without replacement, what is the probability that at least one glove will be right-handed? (1) 6. 7. A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 25%. She also believes that if the economy encounters recession, the probability that her mutual fund will increase in value is 20%. If there is no recession, the probability that the mutual fund will increase in value is 75%. Find the probability that the mutual fund’s value will increase. (0.6125) 1 55 and that a student works more than 10 hours per week is 0. find the probability that the patient is the following. drives to work and is a homeowner? (0. 9. If these two events are independent. the results were reported as the following: 2 . two cars are selected at random from these 44 cars. does not drive to work or is a renter? (0. b) female or works for more than 10 hours per week.5909) Now.5475) c) Given that the respondent drives to work. iii. a non-alcoholic.000 homeowners and 1.8. Find the probability that at least one of these cars have GPS navigation system.000 renters.5880) b) Given that the respondent drives to work. what then is the probability that he or she is a homeowner? (0.62. drives to work? (0. a) If a patient is selected at random. i. Drives to Work Yes No Homeowner 824 176 Renter 681 319 a) If a respondent is selected at random. 11. One of the 44 cars is selected at random. 10. find the probability that a randomly selected student is a a) male and works for more than 10 hours per week.7525) ii. 18 of which have a GPS navigation system. and 200 non-alcoholic patients. Due to the devaluation which occurred in country PQR. Based on a study conducted. The probability that a randomly selected student from college is female is 0.4525) d) Are the two events.4091) b) does not have a GPS navigation system. A car rental agency currently has 44 cars available. A recent study of 300 patients found that of 100 alcoholic patients. an alcoholic with elevated cholesterol level. a non-alcoholic with non-elevated cholesterol level. what if the probability that he or she i.4120) iii. find the probability that this car. what then is the probability that he or she is a renter? (0. ii. a) has a GPS navigation system. the consumers of that country were buying fewer products than before the devaluation. b) Are the events “alcoholic” and “non-elevated cholesterol levels” independent? Are they mutually exclusive? Explain why or why not. 43 had elevated cholesterol levels. Suppose that the survey consisted of a sample of 1. (0. driving to work and the respondent is a homeowner. (0. A housing survey studied how City Sun homeowners get to work. 87 had elevated cholesterol levels. independent? (not independent) 12. 24) purchased more products and changed brands? (0. A soft-drink bottling company maintains records concerning the number of unacceptable bottles of soft drink from the filling and capping machines.02) given that a consumer changed the brands they purchased. If a filled bottle of soft drink is selected at random.60.04. the probability that a bottle came from machine I and was non-conforming is 0. what then is the probability that the consumer purchased fewer products than before? (0.7443) 13. a) Draw a tree diagram to illustrate the above events.0417) b) What is the probability that the car needs a warranty repair given that Country ABC did not manufacture it? (0. It is known that 168 of them are male. 40% of male sale agents has permanent job while half of female sale agents do not have permanent job.0025. CASTWAY is a direct selling company which has 350 authorized sale agents from all over the country. what is the probability that it is non-conforming? 14. Based on past data. a) What is the probability that the car needs a warranty repair given that Country ABC manufactured it? (0.Brands Purchased Same Changed Number of Products Purchased Fewer 10 262 Same 14 82 More 24 8 What is the probability that a consumer selected at random: a) purchased fewer products than before? (0.0125) b) c) d) it was filled on machine I and is a conforming bottle? (0.99) it was filled on machine II or is a conforming bottle? suppose you know that the bottle was produced on machine I. the probability that the car manufactured by Country ABC is 0. has permanent job? ii. Each year. Based on a study. is a male given that he does not have permanent job? 3 . ratings are compiled concerning the performance of new cars during the first 90 days of use.0375) c) Are need for a warranty repair and country manufacturing the car statistically independent? (not independent) 15.025. i. b) What is the probability that a randomly selected sale agent. and the probability that the new car needs a warranty repair and was manufactured by Country ABC is 0. the probability that the new car needs a warranty repair is 0.01 and the probability that a bottle came from machine II and was non-confirming is 0. what is the probability that a) it is a non-confirming bottle? (0.68) b) c) d) purchased the same number or same brands? (0. fill water in the bottle (B) and tug & war (T). There are run with one leg (G). Given P(M) = 0. c) Is event M and event N are independent event? Prove it The organizer has organized three games during the Lam’s family day. (5) iii. Participate in tug & war game given he/she has participated in run with one leg game. Value of a.20 M 0. The number of participant who participate in one game only.33. (3) ii. 4 . find the probability the participant. Participate in fill water in the bottle game and run with one leg game only.25 M 0.58 and P(MN) = 0. The number of participant who participate more than one game.22 M a) Complete the Van Diagram above with the probabilities value.53. Participate in all games iii. (24) b) If one participant has been selected at random.EXERCISE 2 (CHAPTER 3) 1. find: i.33 M 0. S M N 0. 40 participants had participated in these games. i. S B 9 2a 5 2a 7 5 T G 2 a) Based on the Diagram above. Below is the Vann Diagram shown the number of participants for every game during the family day. ii. The number of participant who participate in tug & war only. b) Is event M and event N are mutually exclusive? Prove it. P(N) = 0. 2. (16) iv. 5 . i. Xpress Link is a courier company with 300 staff with the qualification level shows in the Van diagram below. singing. a) Find the number of staff who holds diploma and bachelor degree only. Below is the Van Diagram for 100 contestants during these competitions. a) Find the number of contestants who participated in dance and act contests. singing 20 2a 5 18 a 15 act 12 dance Based on the Venn diagram.84) ii. (k=16) b) What is the probability one staff who has been selected at random holds. i.47) more than one contest (0.0533) c) Is the staff holds diploma and master degree is an independent event? Prove it.57) singing contest given he/she had join in act contest except dance contest. dance and act contests. bachelor degree diploma 36 2k k 4k 50 master degree 102 Based on the Vann diagram above. three qualifications. ii. (a=10) b) If one contestant has been selected at random. what is the probability the contestant participate in. qualifications except master degree (0. one contest only (0. iii. (0.3. Harmony Cultural Club has organized three competitions. iv. Some of the staffs hold more than one qualification. The competition has been organized during the different time and each contestant can participate more than one contest. 4. 5. Company R S T Total Ship Type Cargo 20 40 30 90 Passenger 20 20 40 80 Total 40 60 70 a) Find the probability choosing a cargo ship from company S b) Find the probability choosing a ship belong to the company T given that the ship is a passenger ship. all are cargo ships ii.4 b) P(A B) = 0. Given two radios has been sold last week. There are three shipping company in Baltravia country. company R. 5% from the total radio sales at the Nora’s electric shop will be returned back for repair by the buyer because the malfunctions of the radio in first six month.3. all are from the same type of ships. Then.2. 6 . c) Build the tree diagram to show the selection of a ship from each company. 6. the second radio will be returned back for repair given the first radio had been return for repair. Draw the Venn diagram to represents this statement. d) Based on the answer (c). none of the radio has been returned back for repair iii. P(B) = 0. c) Are the events returning back both the radios for repair is independent event? Prove it. These three companies have a cargo ship and passenger ship. find: a) P( B ) = 0.7 c) P(B|A) = 0. Given P(A) = 0. 7. both radios will be return back for repair ii. S and T.6 and P (A B) = 0. find the probability: i. Table below shows the information about the companies.67 d) P( A B) e) Are A and B is mutually exclusive? Prove it. one of the radio will be returned back for repair iv. b) Find the probability that: i. a) Draw the tree diagram to represent the above event. Two shooters have been selected to represent Malaysia in USIA game. what is the probability he has used the plan B? 9. The probability the first shooter bid the target is ½ and the probability second shooter miss the target is 1/3. Then. Draw the tree diagram to represent the events. A marketing manager wants to promote a new product of his company named Osom. The probability he will choose plan A is 1/3. a) Draw the tree diagram to represent the situation b) What is the probability that he does not succeed to promote the product? c) If he fails to promote the product. find the probability: a) first shooter and second shooter bid the target b) only one shooter bids the target c) none of the shooter bid the target 7 . The probability he does not succeed to promote the product when using plan A and plan B is 1/5 and 1/6. He has two marketing plan which are plan A and plan B. The game will be started by first shooter and followed by the second shooter.8.