Multiple choice
A multiple choice test has 50 questions, with 4 answer choices each. You must get at least 30 correct to pass the test, and the questions are very difficult.
a) Are you likely to be able to pass by guessing on every question? Explain.
b) Suppose, after studying for a while, you believe you have raised your chances of getting each question right to 70%. How likely are you to pass now?
c) Assuming you are operating at the 70% level and the instructor arranges questions randomly, what is the probability that the third question is the first one you get right?