Exercise 8.9 A restaurant sells three different types of dessert: chocolate, brownies, yogurt with seasonal fruits, and lemon tart. Years of experience have shown that the probabilities with which the desserts are chosen are 0.2, 0.3, and 0.5, respectively. (a) What is the probability that out of 5 guests, 2 guests choose brownies, I guest chooses yogurt, and the remaining 2 guests choose lemon tart? (b) Suppose two out of the five guests are known to always choose lemon tart. What is the probability of the others choosing lemon tart as well? (c) Determine the expectation and variance assuming a group of 20 guests.
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- Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the men interviewed, 20% had asked for a raise and 64% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, find the following probabilities. (Enter your answers to three decimal places.) (a) P(man asked for a raise) (b) P(man received raise, given he asked for one) (c) P(man asked for raise and received raise)A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $30,000, a $125 gas card, or a $5 shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership's showroom. The fine print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,729, the chance of winning the gas card was 1 out of 31,729, and the chance of winning the shopping card was 31,727 out of 31,729. Complete parts (a) through (d). a. How many fliers do you think the automobile dealership sent out? Assume there is one car and one gas card available. 31729 fliers C b. Using your answer to (a) and the probabilities listed on the flier, what is the expected value of the prize won by a prospective customer receiving a flier? H=$5.95 (Round to the nearest cent as needed.) c. Using your answer to (a) and the probabilities…(a) Student A would like to visit a country where 92% of the population speaks the native language. However, Student A does not speak and understand that language. What is the probability that at least two of three locals at the immigrant department of the airport will succeed to communicate with Student A? Answer = Answer (b) Research Scientist A investigates the infected laboratory rats in modeling human diseases. Research Scientist A finds out the probability of the laboratory rats getting infected is two out of ten. What is the probability that five laboratory rats must be required before Research Scientist A finds at least three laboratory rats but not all have been infected? Answer = Answer (c) A badminton game consists of at least two matches, and each match consists of 21 points. The probability of Player A and Player B earning a point in their matches are 80% and 90%. What is the probability difference between Player A and Player B to get their second points within…
- Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can’t recall the brand name and does not wish to return home to find the old can of paint. So, she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand? Her husband also goes to the paint store and fails to remember what brand to buy. So, he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband’s selections independent of the wife’s selections?)Two machines turn out all the paper bags produced in the plant. Machine A produces 38% of the bags and machine B produces 62% of the bags. Machine A produces defective bags 1.9% of the time and machine B produces defective bags 3.8% of the time. Given a defective bag, what is the probability that it came from machine B?A shop keeper sells three models of televisions A, B and C.Sale of model A is 40% of which 3% are with stereo.Sale of model B is 40% of which 7% are with stereo.Sale of model C is 20% of which 9% are with stereo.What is the probability that a randomly sold television is with stereo?
- A large stockpile of used pumps contains 20% that need repair. A repairman is sent to the stockpile of pumps with 3 repair kits. He selects pumps at random and tests them to determine if they need repair. If the pump works corretly, he goes on to the next pump. If the pump does not work, he repairs it with one of his repair kits. (a) Determine the probability that he uses his last repair kit after testing the 7th pump. (b) It takes 10 minutes to test a working pump and 30 minutes to test and repair a pump that is not working, find the expected amount of time that the repairman will need before he uses all 3 repair kits.A student takes a multiple-choice quiz with 5 questions, each with four possible answers and only oneof them is correct. A passing grade is 60% or better (i.e., answering at least 3 of 5 questions correctly).Suppose that the student was unable to find time to study for the exam and just guesses at eachquestion. Find the probabilities for the two events below.i. the student gets exactly 3 questions correct.ii. the student passes the examA geologist has collected 19 specimens of basaltic rock and 19 specimens of granite. The geologist instructs a laboratory assistant to randomly select 33 of the specimens for analysis. (a) What is the pmf of the number of granite specimens selected for analysis? (Round your probabilities to four decimal places.) P(x) (b) What is the probability that all specimens of one of the two types of rock are selected for analysis? (Round your answer to four decimal places.) (c) What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? (Round your answer to four decimal places.)
- The accidents that occur in a manufacturing company were classified by severity (strong, moderate and mild) and by sex with the following characteristics: 40% of the accidents were strong and 30% were moderate. Women suffered 20% of the accidents. Of the total number of serious accidents, men suffered 85.5% of the accidents. Similarly, of the total moderate accidents, women suffered 45% of the accidents. Calculate the following probabilities:- If a woman suffered an accident, what is the probability that it was minor?- If a man suffered an accident, what is the probability that he is strong?A market in Boston orders oranges from Florida. The oranges are shipped to Boston from Florida by either railroad, truck, or airplane; an order can take 1, 2, 3, or 4 days to arrive in Boston once it is placed. The following probabilities have been assigned to the number of days it takes to receive an order once it is placed (referred to as lead time): Lead Time Probability 1 .20 2 .50 3 .20 4 .10 1.00 Compute the expected number of days it takes to receive an order and the standard deviation.A social event allows free entrance to those with Aim High credit card or those with the car Elite. The probabilities of having Aim High and Elite among the employees of a company are 0.10 and 0.05, respectively. Having Aim High is found to be independent of owning Elite. If 1,000 invitations are sent randomly to employees of the company, estimate the number who will be given free entrance.