A manufacturer of cotter pins knows that $5 \%$ of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is

Poisson distribution is a probability distribution which is obtained when the probability (p) of the happening of an event is same in all the trials and there are only two events in each trials generally says successes and failures probability (p) of the happening of the event in trial is very less but number of trials $(\mathrm{n})$ is very large. Here, $\mathrm{p}=5 \%=\frac{5}{100}=\frac{1}{20}$ is very less and $\mathrm{n}=100$, is very large. Hence, one has to employ the Poisson distribution in the given question.