Consider a cluster of 10 computers. Let p be the independent probability that a

Question

Consider a cluster of 10 computers. Let p be the independent probability that a computer is up (working) and 1-p be the independent probability that a computer is down (not working) (a) Write an cxpression for the average number of computers that are up. (b) Write an expression for the probability that at least 1 computer is up (there are two ways this can be done) (e) Suppose now that there are two independent clusters of 10 computers each. Write an expression that at least one computer is up in EACH cluster.

Explanation / Answer

Solution:

Given:

n = 10 computers

p = probability of success

1-p = probability of failure

a)

Using Binomial distribution:

mean = average = np = 10p

b)

For atleast one computer being up:

1- none is up

= 1 - 10C0 + p^0 * (1-p)^10

= 1-(1-p)^10

c)

1- none is up in each cluster

=>

2 * (1-(1-p)^10)

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