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An experimental file server is up $75$% of the time and down for $25$% of the time due to bugs. How many times does this file server have to be replicated to give an availability of at least $99$% ?

1. $2$
2. $4$
3. $8$
4. $16$

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Lets us check each option

• a) if there are 2 replications, probability of failing both at same time = .25*.25 = .0625 =6.25%
Availiability = 100-6.25=93%  //Not the answer
• b) In case of 4 replications probability of failing all at same time =(0.25) 4 =0.0039=0.39%
Availiability = 100-0.39 ~ 99% //Hence the answer

No need to check furthur as all options are more than 4

by
25%=0.25....down tine

100%-99%=1%... this translates to 0.01

therefore, no. of replications = n log (0.25)= log 0.01

n = (log(0.25)) / ( log (0.01))

= 4 replications

+1 vote