A company buys microchips from three suppliers I, II and III. Supplier I has a record of providing microchips that contain 10% defective; supplier it has a defective rate of 5% and supplier III has a defective rate of 3%. Suppose 10%, 40% and 50% of the current supply came from suppliers I, II and III, respectively. If a randomly selected microchip is defective, what is the probability that it came from supplier II? Express your answer accurate to two decimal places. O 48 O.40 O something else O 44 O 41
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- In a town, there are three bridges: Bridge A, Bridge B, and Bridge C. On any given day, the probability of each bridge being open for passage is as follows: P(A) = 0.4, P(B) = 0.3, and P(C) = 0.5. If a resident needs to cross all three bridges in succession, what is the probability of successfully crossing all three bridges without encountering any closures?Thirty six percent of all assembly line mechanical robots are claimed for services by the technicians to be sent out to the manufacturer all under the issued warranty at the time of purchase. Out of these robots sent under warranty, 45% will be repaired and sent back to the factory and 55% will be replaced under warranty at no cost. Suppose the company you are working for recently ordered 15 of these mechanical robots. The CEO agreed to sign a five years purchasing contract if only the probability of sending back three of these robots are LESS than 0.24 during the life of the contract. Will she approve the purchasing contact?The three-year recidivism rate of parolees in a certain state is about 20%; that is, 20% of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below. Find the probability that exactly 6 out of 20 parolees will end up back in prison within three years. The probability that exactly 6 out of 20 parolees will end up back in prison is nothing.
- The proprietor of Midland Construction Company has to decide between two projects. He estimates that the first project will yield a profit of $160,000 with a probability of 0.7 or a profit of $120,000 with a probability of 0.3; the second project will yield a profit of $220,000 with a probability of 0.6 or a profit of $70,000 with a probability of 0.4.Find the expected profit for each project. first project $ second project $ Which project should the proprietor choose if he wants to maximize his expected profit? first project second projectA company sends its products from 3 warehouses, namely from warehouse A=30%, warehouseB=20% and from warehouse C=50%. Based on complaints from customers, it is known thatthe percentage of defective products sent from each warehouse is as follows: A=3% , B= 5% and from warehouse C= 2%.a. Suppose a customer after ordering the product, the next dayComplained that the item was defective. What is the probability that the product receivedthe customer is from warehouse C? b. If another customer who also orders the product and getsthe goods are in good condition, what is the probability that the product received by the customerdoes it come from warehouse A?suppose that a finished product is randomly selected. What is the probability that 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively, are defective. Now, In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and and 2% of the products made by each machine, respectively, it is defective?
- 3. You get a haircut from Barber Shop 1 30% of the time and Barber Shop 2 70% of the time. Barber Shop 1 gives a good haircut 80% of the time and a bad haircut 20% of the time while Barber Shop 2 gives a good haircut 90% of the time and a bad haircut 10% of the time. For any given haircut, the probability that it is a bad haircut from Barber Shop 1 is Barber Shop 2 is and the probability that it is a good haircut from O.06; .63 .2; .73 O.06; .73 .2; .63On any given morning here at Chabot College, coffee is brewed in the Science and Math Division workroom by one of two faculty members, depending on who arrives first at work. Instructor Yest arrives first 75% of the time. Instructor Kelly arrives first the remaining mornings. The probability that the coffee is brewed strong when brewed by Instructor Yest is 0.2. The probability that the coffee is brewed strong when brewed by Instructor Kelly is 0.9, as Instructor Kelly likes her coffee strong! Given the coffee is strong on a randomly selected morning, what is the probability that is was brewed by Instructor Yest?Dom's Pizza Company uses taste testing and statistical analysis of the data prior to marketing any new product. Consider a study involving three types of crusts (thin, thin with garlic and oregano, and thin with bits of cheese). Dom's is also studying three sauces, (standard, a new sauce with more garlic, and a new sauce with fresh basil). The probability that a judge will get a plain thin crust with a standard sauce for his first taste test is
- 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?You are a physician meeting with a patient who has just been diagnosed withcancer. You know there are two mutually exclusive types of cancer that the patientcould have: type A and type B. The probability that she has type A cancer is 1/3. TypeA is deadly: four patients out of five diagnosed with type A cancer die within one year.Type B is less dangerous: only one patient out of five diagnosed with type B cancerdies within one year. What is the probability that your patient has type A cancer and suc-cessfully survives it? What is the probability that your patient dies within a year? Suppose that your patient dies in less than one year before you learn the exact type of cancer he has. Given this sad happening, what is the probabilitythat she had type A cancer? (Hint: You want to start off by considering this question: given the informationprovided in the story (what those numbers are really about?), which of the twoanalytical tools we have covered in class will be more helpful to solve…Maximus Steel plans to introduce one of three new products code-named: Wren, Hawk, and Nightingale. The marketing department indicated that the success of any product depends on the market conditions (Favorable, Neutral, or Unfavorable). The profit the company will earn also depends on the market conditions. The table below shows the probability estimated for each market condition and the profits Maximus Steel will realize within those conditions: Product Code Market Conditions Favorable P = 0.2 Neutral P = 0.7 Unfavorable P = 0.1 Wren $120,000 $70,000 ($30,000) Hawk $60,000 $40,000 $20,000 Nightingale $35,000 $30,000 $30,000 Maximus Steel is considering hiring a market research firm to do a survey to determine future market conditions. The results of the survey will indicate either positive or negative market conditions. There is a 0.60 probability of a positive report, given favorable conditions; a 0.30 probability of a positive…