ECE 558 - Spring 2021

Power System Reliability

Project 1 - Due 4 Feb 2021

1. The probability of Inspector 1 on a production line finding a defective item is 0.8 and of Inspector 2, down the line, 0.7. What is the probability of a defective item getting through?
2. A pair of fair dice is tossed. Find the probability that at least one of the two numbers is greater than 4.
3. Three persons work independently at solving a given design problem. The respective probabilities that they solve it are 1/4, 1/3, 1/2. What is the probability that the problem will be solved?
4. A worker operates three machines. The probability that for the duration of an hour a machine does not require the attention of the worker is 0.9 for the first machine, 0.8 for the second, and 0.85 for the third.
   1. What is the probability that in any one hour none of the machines requires the worker's attention?
   2. What is the probability that at least one of the machines does not require any attention during any one hour?
5. A piece of equipment contains six identical items and it is known that three of them are defective. The items are tested one after the other until the three defective items are found.
   1. What is the probability that the testing process stopped on the (i) third test (ii) fourth test?
   2. If the process is stopped on the fourth test, what is the probability that the first item is not defective?

Main Campus students must submit their assignments on paper at the beginning of the lecture. In addition, both Internet students and Main Campus students must submit an electronic copy via SafeAssignment on the ECE 558 Blackboard site BEFORE the beginning of class. SafeAssign does not allow multiple files, so you need to submit a single file, such as a PDF or a Word Document with suitably compressed scanned images (e.g., JPEG). Make sure your file is less than 1 MB in size!