Question

A company uses five backup servers to secure its data. The probability that a server fails is 0.13. Assuming that the failure of a server is independent of the other servers, what is the probability that one or more of the servers is operational

Answer 1

Probabilities are used to determine the chances of events

The probability that one or more of the servers is operational is 0.99996

How to determine the probability

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

$P(0) = 0.0000371293$

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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