A calculator manufacturer checks for defective products by testing 3 calculators out of every lot of 12. If a defective calculator is found the lot is rejected.
a) Suppose 2 calculators in a lot are defective. Outline two ways of calculating the probability that the lot will be rejected. Calculate this probability
(Do I use the probability distribution here? This question is a hypergeometric distribution
b) The quantity control department wants to have at least 30% chance of reject lots that contains only one defective calculator. Is testing 3 calculators in a lot of 12 sufficient? If not how would you suggest they alter their quality control techniques to achieve this standard? Support your answer with mathematical calculations