Question

There are two independent file servers in a web site. Either file server works with a probability of 0.6. And this web site is up if either file server is working. The probability that the web site is up is _____.

Answer 1

Answer:

The probability that the web site is up is 0.84 = 84%.

Step-by-step explanation:

For each web server, there are only two possible outcomes. Either it is working, or it is not. The probability of a web server being working is independent of any other web server, which meas that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Either file server works with a probability of 0.6.

This means that $p = 0.6$

Two servers.

This means that $n = 2$

The probability that the web site is up is

At least one server working, which is:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.6)^{0}.(0.4)^{2} = 0.16$

Then

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.16 = 0.84$

The probability that the web site is up is 0.84 = 84%.