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maggie2
03-22-2006, 09:40 AM
I have a question that i'm having a really hard time even starting.

The IT department runs 3 redundant computer servers concurrently. For each server there is a 14% chance of crashing in a given day. Assume that a server crashing is independent from any other server crashing.

a.) What is the probability that none of the 3 servers will crash for 7 consecutive days?

b.) What is the probability at a least one server will crash in a 7 consecutive day period?

My thought on the first question would be that there is an 86% chance that the server will not crash. If I had the three probabilities that will give me the probability for one day. Then I multiply by 7? Am I even close?

There are two more sections to this problem but I'm hoping that if I figure out how to set up the first two parts i'll understand the other two.

Any help would be appreciated.

WeeG
03-25-2006, 02:33 PM
let's say that:

A - server number 1 will not crash in a given day
B - server number 2 will not crash in a given day
C - server number 3 will not crash in a given day

P(A&B&C) = (0.86)^3 = 0.6360 = P'

so P' is the probability that none of the servers will crash in a given day.
you are looking for the probability that P' will accure 7 days in a row.

n = 7
p = P'

you can use the binomial distribution or just a simple logic to calculate the needed probability...
I think, it is confusing ! :)