Oxnard Casualty wants to ensure that their e-mail server has 99.98 percent reliability. They will use several independent servers in parallel, each of which is 95 percent reliable. What is the smallest number of independent file servers that will accomplish the goal?

The smallest number of servers required is 3 servers

Explanation:

Given

Required

Minimum number of servers needed

Let p represent the probability that a server is reliable and the probability that it wont be reliable be represented with q

Such that

It should be noted that probabilities always add up to 1;

So,

'

Subtract p from both sides

Substitute

Convert % to fraction

Convert fraction to decimal

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To get an expression for one server

The probabilities of 1 servers having 99.98% reliability is as follows;

Recall that probabilities always add up to 1;

So,

Subtract q from both sides

So,

Let the number of servers be represented with n

The above expression becomes

Convert percent to fraction

Convert fraction to decimal

Add to both sides

Subtract 0.9998 from both sides

Recall that

So, the expression becomes

Take Log of both sides

From laws of logarithm

So,

becomes

Divide both sides by

Hence, the smallest number of servers required is 3 servers