At a toy factory, 34% of all the produced toys go through an automated camera-based inspection and 25% of the toys go through manual inspection. Each toy either goes through only one of those inspections or is not inspected at ll. In other words, the remaining 41% otf the toys are not inspected, it is known that toys that are inspected automatically have no defects with probability 0.90 and toys that are inspected manually have no defects with probability 0.92. Manufactured toys that do not go through an inspection have no defects with probability 0.73. a. What is the probability that a randomly bought toy in a store, which is a product of this factory, is defective? b. A customer buys a toy manufactured at this factory and finds defects in it. What is the probability that this toy went through an automated camara- básed inspection?

At a toy factory, 34% of all the produced toys go through an automated camera-based inspection and 25% of the toys go through manual inspection. Each toy either goes through only one of those inspections or is not inspected at ll. In other words, the remaining 41% otf the toys are not inspected, it is known that toys that are inspected automatically have no defects with probability 0.90 and toys that are inspected manually have no defects with probability 0.92. Manufactured toys that do not go through an inspection have no defects with probability 0.73. a. What is the probability that a randomly bought toy in a store, which is a product of this factory, is defective? b. A customer buys a toy manufactured at this factory and finds defects in it. What is the probability that this toy went through an automated camara- básed inspection?

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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A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 52 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is ______ (Round to four decimal places as needed.) The company will accept ____% of the shipments and will reject ____% of the shipments, so______________ (many of the shipments will be rejected or almost all of the shipments will be accepted. (Round to two decimal places as needed.)
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