Problem 3: You work for a company looking to hire programmers. You want to hire the best person for the job. but you don't want to end up with a situation where you potentially have to hire everyone. Assume that you have a list of candidates of length n. 1. Under the old strategy of always hiring the best person, how many hires would you need to make before the probability that you hire nobody new decreases below 1A? Under the old strategy of always hiring the best person, how many hires can you make while the probability that you will still hire someone new remains more than 36? Suppose you're comfortable hiring someone who isn't the best, but only with some small probability P. Write pseudocode for an algorithm that hires at most O(log(n)) employees and hires the best one with probability 1 P, where P is considered as a constant. Express the runtime of your algorithm as a function of both a. and the parameter P. (You could imagine a case where the P you care about changes with n, so it is good to explicitly show how Ol') depends on P.)