Items are packaged in boxes of 100 each. A sampling inspection plan calls for rejecting a box if a sample of 5 drawn from that box contain 1 or more defectives. What is the probability that a box containing exactly 4 defectives is rejected?
I determined that the probability of a defective = $4/100 = .04$, call this $q$, and the probability of not defective = $.96 = p$.
In a sample of 5, I decided the probability of at least one defective is: $$\sum_1^5 \binom{5}{n}p^nq^{5-n} = 1 - .96^5 = .184627$$
The answer provided in the book is $.19$. If I were to round to the nearest hundredth, I'd have $.18$. Is this just a rounding issue or is there something wrong with my approach?