Probabilities are used to determine the chances of events
The probability that one or more of the servers is operational is 0.99996
The given parameters are:
n = 5 --- the number of backup servers
p = 0.13 -- the probability that a server fails
Start by calculating the probability that all the 5 servers fail
P(0) = 0.13^5
[tex]P(0) = 0.0000371293[/tex]
The probability that one or more of the servers is operational is then calculated using the following complement rule
P(1 or more) = 1 - 0.0000371293
Evaluate the difference
P(1 or more) = 0.99996
Hence, the probability that one or more of the servers is operational is 0.99996
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