Question: Friends Phoebe and Fiona fiddle with fiery flares for fun ... at work as engineers. They have noticed that each batch of 400 typically has four that are irregular in some way, or simply misfire when activated. While their group guru, Geraldine, has a team of colleagues working on reducing this defect rate, the two friends are dealing with the current manufacturing reality. (a) Phoebe wonders about the chance that she might have to select 75 flares in order to find a defective flare in a lot. What is this likelihood? (b) Fiona wonders about accepting these lots of 400 for shipment. If she wants to approve a lot for shipment only if she finds no defects in her sample, then how large a sample must she select in order to have a less than 10% chance that the lot contains at least one defective flare? [COMMENTS & HINTS: For each part of this problem, which discrete probability distribution is appropriate?]