Basic Statistics20815 marksNumerical: Bayes theorem probabilityConditional probability and Bayes theorem
A database server has a 95% reliability rate. Even if the server does not fail, there is a 5% chance that it will still report an error. If the server reports an error, what is the probability that the server has actually failed? P(textFailure) = 0.05, quad P(textFalse positive) = 0.05
A database server has a 95% reliability rate. Even if the server does not fail, there is a 5% chance that it will still report an error. If the server reports an error, what is the probability that the server has actually failed? $P(\text{Failure}) = 0.05, \quad P(\text{False positive}) = 0.05$ [5]
- Server reliability = 95%, hence probability of failure: $$P(F) = 0.05$$ - Probability of no failure: $$P(\bar{F}) = 1 - 0.05 = 0.95$$ - False positive rate (error reported even though no failure): $$P(E \mid \bar{F}) = 0.05$$ - Assumption from problem statement: if the server fails, it reports ...