Aweb server hosting company advertises 99.999 percent guaranteed network uptime. (a) how many independent network servers would be needed if each has 97 percent reliability? (round your answer up to the nearest whole number.) network servers (b) how many independent network servers would be needed if each has 88 percent reliability? (round your answer up to the nearest whole number.)

The solution for this problem would be:
Given that there is 99.999%.

Let denote n as the network servers and p as the reliability of each server.
So the probability that the network uptime = 1 - (1 - p)^n

Therefore, (1-p) ^n = 0.00001

a. x= log(1-.99999)÷log(1-.97)= 3.2833 is the answer

1-(1-.97)^3= 0.99999 + 0.0001 = 1

b. x = log(1-.99999)÷log(1-.88) = 5.43 is the answer

1-(1-.88)^3= 0.99 + 0.0001 = approx 1

/-/////////looks tough ‍♂️