Problem 2.3 (Video 1.6) You would like to evaluate the probability of success for testing a batch of n widgets. To start out, let's assume that if there is a problem with the batch, exactly 1 out of the n widgets are defective. You are willing to test only k of the widgets (due to budget or times constraints). (a) How many ways are there of testing k out of n widgets? (b) How many ways are there of testing k widgets with the defective widget included? (c) Use your answers from parts (a) and (b) to determine the probability of catching a defective batch. (d) Evaluate your answer from part (c) for n 20 and k = 5. (e) Now, say that a defective batch contains exactly 2 defective widgets. How many ways are there of testing k widgets with at least one defective widget included? (You may assume that k > 2.) (f) Use your answer from part (e) to determine the probability of catching a defective batch. (g) Evaluate your answer from part (f) for n = = 20 and k = 5.