Two servers, one website, better uptime

Question

A website runs on two independent servers. The site is reachable as long as at least one server is up. Each server is up with probability 0.9 at any given moment, independently of the other.

What is the probability the website is reachable?

Accepted Answer

"At least one up" is easiest through its complement, "both down." Since the servers fail independently, P(	ext{both down}) = 0.1 	imes 0.1 = 0.01. Therefore P(	ext{site up}) = 1 - 0.01 = 0.99. A single server gives 90% uptime; adding one independent backup lifts it to 99%, cutting the downtime tenfold, from 10% to 1%. Takeaway. For "at least one works" among independent components, multiply the failure probabilities and subtract from 1. Redundancy attacks the product of failure rates, which is why a cheap backup can slash outage time dramatically.

Two servers, one website, better uptime

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