I think it depends on how you define availability. 1. Suppose we define availability as "at least one is up". If the failures are completely independent, then

I think it depends on how you define availability. 1. Suppose we define availability as "at least one is up". If the failures are completely independent, then the probability of any one being down is 10^-5 (five nines) and the probability of all 10 being down at the same time is (10^-5)^10 = 10^-50 (fifty nines). 2. If we instead define availability as "all 10 are up" (which is essentially equivalent to one failure causes a cascading failure) then in the same scenario where failures are independent, this is (1-10^-5)^10 ~= 99.99% (four nines).