The arithmetic in reverse
Redundancy runs that same arithmetic in reverse. If either of two independent copies can serve the request, you fail only when both fail.
Two nodes at 99.9 percent each, so each carries a one in a thousand chance of being down. Both down together is one in a million, which makes the pair 99.9999 percent available. One duplicate bought you three extra nines.
The asymmetry is the entire it is the entire economic case for replicas and multiple regions. Chaining things costs you a little. Putting them in parallel pays enormously.
The formula generalises: with several copies each failing with some probability, your availability is one minus that probability raised to the number of copies. Three unimpressive 99 percent servers in parallel give 99.9999 percent. Cheap unreliable things in parallel beat expensive reliable things standing alone, and that is what commodity cloud hardware was built on.
The fine print
Now read the fine print, because interviews and production both punish people who stop at the formula. It assumes failures are independent, and real failures correlate.
What your copies share matters. Two replicas in one rack share a switch. Two availability zones share a region's control plane. And every copy shares your deploy pipeline and your configuration, which matters because bad deploys and bad config cause more outages than hardware ever does. Your two 99.9 percent nodes are one careless config push from failing together.
Failover has an availability of its own. Detection takes time, the switchover itself can fail, and a standby you have never exercised is a prayer rather than a plan. Model it as the parallel formula discounted by detection time and by how often failover actually works. That is why serious teams run practice drills: redundancy you have not tested rounds down to zero.
Worked example
Sofia runs infrastructure for a ticketing platform whose single Postgres primary at 99.9 percent keeps blowing the SLA during big on-sales. She adds a hot standby with automated failover and presents the naive math: two 99.9s in parallel is 99.9999 percent, about 31 seconds a year. Her SRE lead makes her test it. In the first game day, failover takes 4 minutes: health checks required three consecutive failures at 30-second intervals, and the standby then refused connections because of a stale config file nobody had exercised. They tighten detection to 20 seconds, fix the config drift, and add a monthly automated failover drill. Real failovers now complete in about 40 seconds, and the pair delivers roughly 99.99 percent. Short of the formula's six nines, 10 times better than one box, and every minute of the gap is explained by measurements instead of hope.