A worker is testing light bulbs at a factory. The probability that a light bulb will be defective is 0.05. Assume that the bulbs' condition (defective or good) is independent of the other bulbs. a. A worker tests 3 bulb, find the probability that none of the three bulbs are defective? If the worker tests 10 bulbs, find the probability that exactly one bulb is defective. b. c. If the worker tests 50 bulbs, find the probability that the worker finds at least one defective bulb. d. The worker tests a bulb and finds that it is defective. What is the probability that the next bulb will be defective? Prove that A U (B n C) = (AUB) n (AUC).