GATE 2014 CS (CS2) – Question 11
An IT-office security system has 10 computers, exactly four working. Officials inspect four chosen uniformly without replacement. The system is deemed functional if at least three inspected computers work. If this has probability p, find 100p.
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Correct answer: 11.85 to 11.95
Explanation
Of C(10,4)=210 equally likely samples, exactly three working machines can be chosen in C(4,3)C(6,1)=24ways, and four working machines in one way. Thus p=25/210 and **100p=11.9048**. Sampling is without replacement, so a binomial model would not apply.