Chris recommends her friend to her supervisor for a job. To make her recommendation credible, she can design a test for her friend to take. She can choose the difficulty level of the test by choosing the following two parameters: x = Pr(pass|skilled), and y = Pr(pass|unskilled). Without the test, Chris' friend is believed (by both Chris and her supervisor) to be skilled with probability 0.1. If a skilled candidate is hired, the supervisor gets a payoff of 20. If an unskilled candidate is hired, the supervisor gets a payoff of -10. If no one is hired, the supervisor's payoff is 0. Chris wants to maximize the probability of her friend being hired. (a) (5 points) Would the supervisor hire Chris' friend without the test? (b) (15 points) How would Chris design this test? In other words, what is the optimal value of x and y