GATE 2019 ME (ME2) – Question 50
A manufactured part is defective with probability 0.05. If 15 parts are independently selected at random, find probability of at least two defects, to two decimal places.
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Correct answer: .16 to .18
Explanation
With $X\sim\operatorname{Binomial}(15,0.05)$, use the complement: $P(X\ge2)=1-0.95^{15}-15(0.05)0.95^{14}=0.170953$. Rounded, **0.17**.