In order to test whether a batch of 100 widgets meets specifications, a manufacturer picks 20 items at random. if none are defective, the batch is accepted. if at least one is defective, the manufacturer — whose turns out to be quite unscrupulous — mixes the 20 widgets back in with the 100, then picks 20 more at random. if none are defective, the batch is accepted. if at least one is defective, then the manufacturer finally rejects the batch. if a batch of 100 items has 10 defective widgets, what is the probability that it gets accepted?