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A communication network has a built-in safeguard system against failures.
In this system, if line 1 fails, it is bypassed and line 11 is used.
The probability of failure of any one of these three lines is 0.01,
and the failures of these lines are independent events.
What is the probability that this system of three lines does not completely fail?
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I interpret the given part this way:
There are three lines;
the probability of failure of any one of these three lines is 0.01,
and the failures of these lines are independent events.
If so, then the probability that this system of three lines does not completely fail
is complementary to the probability that all three lines completely fail,
which is 0.01^3 = 0.000001.
Thus the desired probability is 1 - 0.000001 = 0.999999. ANSWER
Solved.
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The post does not present the problem as clear as I interpret it
(and as clear as a Math problem should be presented)
- and it is the problem's fault.
THEREFORE, I have to make some interpretation,
and I did it in a way as I said it.