Problem 2 A student is taking a 10 question multiple-choice test. Each question has 3 wrong choices and 1 correct choice. Suppose that 60 percent of the time she knows the answer and selects the correct choice and the rest of the time she guesses and selects a choice uniformly at random. The student will pass the exam if she gets more than 65% of the questions correct. 1. If she answered a question correctly, what is the probability that she actually knew the correct answer? 2. What is the probability that she will pass? (You may assume inde- pendence between the questions) 3. Her instructor allowed her to continue retaking the exam until she passes. On average, how many times will she need to take it until she passes? (You may, unrealistically, assume independence between test attempts)