Sampling inspection. Suppose that items with a probability p of being acceptable are subjected to inspection in such a way that the probability of an item being inspected is p'. We have four classes, namely, "acceptable and inspected," "acceptable but not inspected," etc. with corresponding probabilities PP Pa P'q, 99 where q = 1-P, 9'-1-p'. We are concerned with double Bernoulli trials [see example VI,(9.c)]. Let N be the number of items passing the inspection desk (both inspected and uninspected) before the first defective is found, and let K be the (undiscovered) number of defectives among them. Find the joint distributions of N and K and the marginal distributions. K