Answer:
The smallest number of servers required is 3 servers
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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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<em>To get an expression for one server</em>
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
<em>Hence, the smallest number of servers required is 3 servers</em>