2. Consider the circuit shown in the figure below where the probability that each device functions correctly is provided. Assume that all devices fail independently. 0.9 0.95 0.9 0.99 b 0.95 0.9 (a) What is the probability that the end points a and b are connected? (b) Suppose that, for some reason, you need to replace the two 0.95-device with two new devices, both have the same probability to function correctly, say p. For what minimum value of p the new devices should be installed to get a and b connected with the probability at least 0.927196875? (Your answer should be an exact number, so do not rounding off every number in the calculation.)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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2. Consider the circuit shown in the figure below where the probability that each device
functions correctly is provided. Assume that all devices fail independently.
0.9
0.95
0.9
0.99
b
0.95
0.9
(a) What is the probability that the end points a and b are connected?
(b) Suppose that, for some reason, you need to replace the two 0.95-device with two
new devices, both have the same probability to function correctly, say p. For what
minimum value of p the new devices should be installed to get a and b connected
with the probability at least 0.927196875? (Your answer should be an exact
number, so do not rounding off every number in the calculation.)
Transcribed Image Text:2. Consider the circuit shown in the figure below where the probability that each device functions correctly is provided. Assume that all devices fail independently. 0.9 0.95 0.9 0.99 b 0.95 0.9 (a) What is the probability that the end points a and b are connected? (b) Suppose that, for some reason, you need to replace the two 0.95-device with two new devices, both have the same probability to function correctly, say p. For what minimum value of p the new devices should be installed to get a and b connected with the probability at least 0.927196875? (Your answer should be an exact number, so do not rounding off every number in the calculation.)
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