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(15) A control system has three assurance nodes, A, B, and C, that switch off if a certain kind of feedback is detected. On an average run of the system, there is a 10% chance of B switching off and a 20% chance that C turns off. Furthermorc, it is known that B and C will mcver turn off on the same run. If cither B or C turn off then there is a 50% chance that A will turn off as well. If you find that the probability of at least one switch turning off is 20%, find the probability that A turns off.

(15) A control system has three assurance nodes, A, B, and C, that switch off if a certain kind of feedback is detected. On an average run of the system, there is a 10% chance of B switching off and a 20% chance that C turns off. Furthermorc, it is known that B and C will mcver turn off on the same run. If cither B or C turn off then there is a 50% chance that A will turn off as well. If you find that the probability of at least one switch turning off is 20%, find the probability that A turns off.

A First Course in Probability (10th Edition)
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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(15) A control system has three assurance nodes, A, B, and C, that switch off if a certain kind of feedback is detected. On an average run of the system, there is a 10% chance of B switching off and a 20% chance that C turns off. Furthermore, it is known that B and C will never turn off on the same run. If cither B or C turn off then there is a 50% chance that A will turn off as well. If you find that the probability of at least one switch turning off is 20%, find the probability that A turns off.
Transcribed Image Text:(15) A control system has three assurance nodes, A, B, and C, that switch off if a certain kind of feedback is detected. On an average run of the system, there is a 10% chance of B switching off and a 20% chance that C turns off. Furthermore, it is known that B and C will never turn off on the same run. If cither B or C turn off then there is a 50% chance that A will turn off as well. If you find that the probability of at least one switch turning off is 20%, find the probability that A turns off.
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