4 Confirmation Bias - 2 points Consider a student who is trying to determine whether the midterm heis currently writing is easy or hard. His prior is that the midterm will be hard with probability > , and easy with probability 2. He believes that individual question difficulty depends on overall exam difficulty as follows: PR(easy question easy exam) = Pr(hard question|hard exam) = PR(hard question easy exam) = Pr(easy question |hard exam) = However, he suffers from the following confirmation bias: anytime he believes that the exam more likely hard than easy, he freaks himself out, and misperceives easy questions as being hard with probability 1 (while also correctly perceiving all hard questions as hard). (a) Explain why he will perceive all questions as difficult. ( point) (b) Show that if he is naively unaware of his bias, he will believe that the exam was difficult with probability greater than 75%. ( point) (c) What if he is sophisticated and is aware of his bias? With what probability will he end up believing that the exam was difficult? (1 point)