Three machines, A, B and C produce 45%, 30% and 25%, respectively, of the total parts produced in a factory. The defective production percentages of these machines are 3%, 4% and 5 % . What is the probability that it occurred with machine C, given that it is defective?
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- A manufacturing company produces two types of smartphones, A and B. 30% of the smartphones produced are type A, while 70% are type B. The defect rate for type A smartphones is 2%, while the defect rate for type B smartphones is 4%. If a customer receives a defective smartphone, what is the probability that it is of type A? Show your calculations and reasoning.A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.96, and the probability that at least one if the two engines does so is 0.98 and the probability that both engine do so is 0.935. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?In the basic science unit of the university, the following results were obtained from 350 students: 200 students passed the differential calculus course 160 passed physics course 187 passed probability-statistics course 112 approved differential calculus and probability-statistics 120 passed differential calculus and physics 95 passed physics and probability-statistics 80 passed the three courses. What is the probability of those who passed only one course? a. 0.051 b. 0.1714 c. 0.38 d. 0.0714
- In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, an average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking sticker holders show up. a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other two lots. Compare two situations: (1) each person can park only in the lot assigned to him or her, and (2) each person can park in any of the lots (pooling). (Hint: Use the RISKBINOMIAL function.) If needed, round your answer to a whole percentage and if your answer is zero, enter "0". No pooling: Pooling: 51.4 % 83.8 % b. Now suppose the numbers of people who show up at…A manufacturing process produces, on the average, 3% defective items. The company ships 15 items in each box and wishes to guarantee no more than 1 defective item per box. If this guarantee accompanies each box, what is the probability that the box will fail to satisfy the guarantee?
- Your assembly plant buys identical widgets from 3 suppliers, A, B, and C. Suppliers A and B each supplies a quarter of your widgets each day, whereas Supplier C supplies the remaining 50%. Of the widgets supplied by A, B, and C, the average numbers of defective widgets are 5%, 3%, and 7%, respectively.(a) If a widget is selected at random, what is the probability of it being defective? Let A, B, C be the event of a randomly picked widget being sourced by suppliers A, B, and C, respectively. Furthermore, let D be the event of a randomly-picked widget being defective. Use these symbols A, B, C, and D when you do this problem.(b) What is the probability of a randomly-picked widget being supplied by A and also being defective?(c) If a randomly-picked widget is defective, what’s the probability of it having been supplied by A?(d) If a randomly-picked widget is defective, what’s the probability of it having been supplied by B? By C? What's the sum of the 3 probabilities…Problem (2): TV or a DVR? A consumer electronics company has observed that 36% of their customers purchased an LED screen television, 26% of their customers purchases a DVR, and 12 percent of their customers purchased both an LED screen TV and a DVR. Find the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR.With regards to a particular gene, the percentage of genotypes AA, Aa, and aa in a particular population are respectively, 60%, 30%, and 10%. Furthermore, the percentages of these genotypes that contract a certain disease are respectively. 1%, 5% and 20%. If a person does contract the disease, what is the probability that the person is of genotype AA?
- The management of the large department store in Example B.1 must determine whether more training is neededfor the customer service clerk. The clerk at the customer service desk can serve an average of three customersper hour. What is the probability that a customer will require 10 minutes or less of service?A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.96, and the probability that at least one if the two engines does so is 0.98 and the probability that both engine do so is 0.935. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?the sales manager knows that 10% of his clients do not pay their debts in full. He supposes that he selects a sample of 100 clients. What is the probability that 14% or more will not be fulfilled in their obligations?