From a large lot of new tires, n tires are to be sampled by a potential buyer, and the number of defectives X is to be observed. If at least one defective is observed in the sample of n tires, the entire lot is to be rejected by the potential buyer. Find n such that the probability of detecting at least one defective is approximately 0.9 if (a) 10% of the lot is defective; (b) 5% of the lot is defective.