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...

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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 7 A large chain retaller purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device Is 10%. If the Inspector of the retaller randomly picks 18 items from a shipment, the probability that there will be at least one defective item among these 18 items is O 0.1501 00.5497 O 0.4503 00.8499
Plz answer all parts correctly asap
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
Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage 0.645 0.099 0.152 0.033 0.611 0.514 0.609 0.523 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.093 0.183 0.064 0.022 Combination 0.071 0.090 0.118 0.042 0.179 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?