A toy company produces a faulty item with a $4\%$ probability. The production control system discards a faulty item with a $99\%$ probability A toy company produces a faulty item with a $4\%$ probability. The production control system discards a faulty item with a $99\%$ probability. Compute the probability that, out of $5$ toys, at least one is faulty and it is not discarded by the production control system. I know from the textbook that the answer is $0,1998\%$, but I can't find the right way of solving the problem.

The probability that a given toy is faulty and not discarded is $$p=.04\cdot.01=.0004$$

The probability that out of $5$ toys, at least one is faulty but not discarded is $$1-(1-p)^5\approx.0019984$$