Ten percent of the tools produced in a certain manufacturing process turn out to be defective. Find the probability that in a sample of 10 tools chosen at random, exactly 2 will be defective, by using the Poisson distribution.

0.184

The correct answer is Option (3) → 0.184

Here $n = 10, p =\frac{10}{100}=0.1$, so $λ = np = (10) (0.1) = 1$.

$P(X = 2) = \frac{e^{-λ}λ^2}{2!} =\frac{e^{-1}1^2}{2} = \frac{1}{2}e^{-1}=\frac{1}{2}(0.368) = 0.184$  [Using Table]