Question

There are $500$ boxes each containing $1000$ ballot papers for election. The chance that a ballot paper is defective is $0.002$. Assuming that the number of defective ballot papers follow Poisson distribution, the number of boxes containing at least one defective ballot paper given that $e^{-2}=0.1353$ is

• A. $216$
• B. $432$
• C. $648$
• D. $234$

Answer 1

Answer: (B)

$432$

Here $\lambda =.002\times 1000=2$
Thus probability that a box contain at least one defective ballot $=1-P(X=0)=1-e^{-2}=1-0.1353=.8647$
Hence number of box out of $500$ which contain at least one defective ballot is $=.8647\times 500=432$