Problem 6 The following table reports the proportions of microchips that a certain PC manufacturer purchases from seven suppliers. a. It is known that the proportions of defective microchips produced by the seven suppliers are 0.001, 0.0003, 0.0007, 0.006, 0.0002, 0.0002, and 0.001, respectively. If a single microchip failure is observed, what are the probabilities that each supplier is responsible? b. Instead assume that all suppliers produce defective microchips at the same rate of 0.0005. If a single microchip failure is observed, what are the probabilities that each supplier is responsible? Supplier S1 S2 S3 S4 S5 S6 S7 Proportion 0.15 0.05 0.10 0.20 0.12 0.20 0.18

Problem 6 The following table reports the proportions of microchips that a certain PC manufacturer purchases from seven suppliers. a. It is known that the proportions of defective microchips produced by the seven suppliers are 0.001, 0.0003, 0.0007, 0.006, 0.0002, 0.0002, and 0.001, respectively. If a single microchip failure is observed, what are the probabilities that each supplier is responsible? b. Instead assume that all suppliers produce defective microchips at the same rate of 0.0005. If a single microchip failure is observed, what are the probabilities that each supplier is responsible? Supplier S1 S2 S3 S4 S5 S6 S7 Proportion 0.15 0.05 0.10 0.20 0.12 0.20 0.18

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Problem 20: The members of a consulting firm rent cars from three rental agencies: 60 percent from agency 1, 30 percent from agency 2, and 10 percent from agency 3. If 9 percent of the cars from agency 1 need an oil change, 20 percent of the cars from agency 2 need an oil change, and 6 percent of the cars from agency 3 need an oil change, what is the probability that a rental car delivered to the firm will need an oil change? And if a rental car delivered to the consulting firm needs an oil change, what is the probability that it came from rental agency 2?
Problem 10 An assembler of computer routers and modems uses parts from two sources. Company A supplies 80% of the parts, and Company B supplies the remaining 20% of parts. From past experience, the assembler knows that 5% of the parts supplied by Company A are defective, and 3% of the parts supplied by Company B are defective. An assembled modem selected at random is found to have a defective part. What is the probability that the part came from Company A? Company B? (adapted from [Mendenhall and Sincich 2016], exercise 3.94).
Question 36 Suppose the voters in a certain city view themselves as follows: 45 percent Conservative (C), 35 percent Liberal (L), and 25 percent Independent (1) The percentage of each group who voted in a particular election follows: 45 percent of Conservatives, 40 percent of Liberals, and 60 percent of Independents. Suppose a person is randomly selected. Find P(V), the probability that the person voted. 49
Question 26 Based on current data (November 2021) the annualized probability of a randomly selected unvaccinated person in B.C. being hospitalized with Covid is 2.68%. The probability for a randomly drawn vaccinated person is 0.135%, and the probability for a partially vaccinated person is 0.723%. Use the ratio of partially vaccinated to fully vaccinated hospitalization probabilities to calculate how much more likely a partially vaccinated person is to be hospitalized. Using two significant digits after the decimal point, the answer is that a partially vaccinated person is about times more likely to be hospitalized.
Question 2: A. A table of joint probabilities is shown below. A1 A2 Аз B1 0.15 0.25 0.20 B2 0.10 0.15 0.15 Page 1 of 6 a. Calculate the marginal probabilities of event A b. Calculate the marginal probabilities of event B c. Calculate P(A1 | B1) d. Calculate P(B1 | A1) e. Calculate P(B1 | B2) f. Calculate P(A1 | A3) g. Calculate P(A1 U B1)
Problem 2 [12 points]: Fourth digit of ID a. Genuine motor company manufactures an assembly which consists of three mechanical components. Suppose that the probability of not meeting specification for the first component is equal to 0.09/ 0.11/ 0.13. For the second and third components the probabilities of not meeting specifications are 0.05/ 0.04/ 0.03 and 0.06/ 0.07/ 0.08 respectively. Assuming that the components are independent in terms of not meeting the specification, determine the probability mass function of the number of components in the assembly that does not meet specification. (6.0) Fifth digit of ID Last digit of ID
QUESTION 2 Three local textile distributors (K, L, and M) are competing for a contract to supply textiles to Company XYZ. The probabilities that textile distributors K, L, and M will win the contract are 0.4, 0.3, and 0.3, respectively. If textile distributors K, L, and M win the contract, the probabilities that they will make profits are 0.65, 0.85, and 0.45, respectively. a) Draw a tree diagram for the above information. b) Calculate the probability that the contract was awarded to textile distributor K given that the contract is found to be unprofitable.
QUESTION 4 Takealot offers 3 types of deliveries: same day, next day and standard. 70% of deliveries are standard, 20% next day and 10% same day. (Costs for same day deliveries are considerably higher than standard delivery costs). Of the next day deliveries, only 1% arrive late. Of the same day deliveries, 2% arrive late. If a record of a parcel is selected randomly, what is the probability that it was a next day delivery and that it was delivered late? Clearly define ALL events before attempting the answer.
QUESTION 12 Based on the following figure (Weighting function), please briefly explain in one or two sentences how each of the following three individuals will react to a prospect with different probabilities: Part (a): Individual X Part (b): Individual Y Part (c): Individual Part (d): Among the three individuals (X, Y, and Z), who is more likely to purchase insurance (i.e., home content insurance or building insurance)? You only need to input X, Y or Z in your answer box Part (e): Please briefly explain your answer to Part (d) in less than 25 word. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 weight 0 X 0.2 For the toolbar press ALT+510 (BC) or ALTHEN+E10 (Mac) 0.4 0.6 probability 0.8 N Sa
Question 9 A batch of 400 LEDS contains 7 that are defective. This is known to be the long-term average for the production. The company sells boxes with 50 LEDS in each box. (a) What is the probability there are 1 or more defective bulbs in a box? (b) If three LEDS are selected at random from a box, what is the probability that the third one selected is defective given that the first one selected was not defective and the second one selected was defective? (c) Boxes are returned if 3 or more are defective. What is the probably a box will be returned?
Problem #8: The backoff torque required to remove bolts in a steel plate is rated as high, moderate, or low. Historically, the probability of a high, moderate, or low rating is 0.57, 0.23, or 0.2, respectively. A sample of 16 bolts are selected for testing. Let X, Y, and Z denote the number of bolts that are independently rated as high, moderate, and low, respectively. Determine the following probabilities. Problem #8(a): Problem #8(b): (a) P(X= 11, Y=2, Z=3) (b) P(X=7| Y= 4) Answer correct to 4 decimals Answer correct to 4 decimals
Question C