Probability of Defective Widgets

A factory produces widgets that may either be defective or non-defective. Historical data shows that 12% of the produced widgets are defective. In a given inspection, 15 widgets are randomly selected.
If you let X be the number of defective widgets in the selected sample, what is the probability that exactly 2 of the selected widgets are defective?

Use the binomial probability formula to calculate this:
$$P(X = k) = {n race k} p^k (1-p)^{n-k}$$ where
- $$n$$ is the total number of trials (15 in this case),
- $$k$$ is the number of successful outcomes (2 defective widgets), and
- $$p$$ is the probability of success on a single trial (0.12 for a defective widget).