The probability that a circuit board fails an electrical inspection is 0.18, independently of every other circuit board. A random sample of n n\,n circuit boards is inspected.
Show that the probability that at least one of the n n\,n cars fails is 1−0.82n1 - 0.82^n1−0.82n.
Find the smallest value of n n\,n for which this probability exceeds 0.99.
State one assumption needed for the binomial model to be appropriate here.