Binomial probability

Suppose that the probability of a company supplying a defective product is a and the probability that the supplied product is not defective is b. Before each product supplied is released for further use, it must be screened through a system which detects the potential defectiveness of the product. The probability that this process successfully detects a defective product is x, and the probability that it does not is y. What is the probability that at least one defective product will pass through the system undetected after 20 products have been screened?

Suppose that the probability of a company supplying a defective product is a and the probability that the supplied product is not defective is b. Before each product supplied is released for further use, it must be screened through a system which detects the potential defectiveness of the product. The probability that this process successfully detects a defective product is x, and the probability that it does not is y. What is the probability that at least one defective product will pass through the system undetected after 20 products have been screened?