Question 1099015: A system is comprised of 5 components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1, x2, x3, x4, x5), where xi is equal to 1 if component i is working and is equal to 0 if component i is failed.
(a) How many outcomes are in the sample space of this experiment?
(b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are both working, or if components 1, 3, and 5 are all working. Let W be the event that the system will work. Specify all the outcomes in W.
(c) Let A be the event that components 4 and 5 are both failed. How many outcomes are contained in the event A?
(d) Write out all the outcomes in the event AW.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! To simplify, I'll just use a five digit number to stand for the vector.
So, 00000 is the vector where all the components are not working.
11111 is the vector where all the components are working.
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a) 5 places, 2 choices so that makes a total of
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b)
1 and 2
11000,11001,11010,11011,11100,11101,11110,11111
3 and 4
00110,00111 01110, 01111, 10110,10111,11110,11111
1,3, and 5
10101,10111,11101,11111
Eliminate duplicates
W={00110,00111,01110,01111,10101,10110,10111,11000,11001,11010,11011,11100,11101,11110,11111}
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c) XXX00, leaves three places with 2 choices,
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d) What does AW mean?
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