In order to fix your computer you need to replace a particular component. You choose possible replacement components from a large box of such components, where each one has a probability 1/4 of working. What is the probability that you have to try at least 5 components before finding the first component that works? Solve this problem in two different ways: (a) Use a finite series to calculate the probability of finding the first working component on the first, second, third, or fourth tries and subtract the result from 1. (b) Use an infinite series to calculate the probability of finding the first working component on the 5th, 6th, 7th, ... tries