Suppose you are taking a multiple choice test with 100 questions, each of which has exactly 5 possible answers. Further suppose that you did not study at all and will have to guess randomly.

a. What is the probability that the 5th question is the first one you answer correctly?

b. what is the expected question # of the first correctly answered question?

c. What is the probability that you answer 2 out of the first 5 questions correctly?

d. What is the probability that you answer 20 out of the 100 questions correctly?

e. What is the expected # of correct questions on the full test?

f. What is the standard deviation of # of correct questions on the full test?

g. Suppose that each correct answer is worth 1 point and each incorrect answer is worth -0.25 points. What is your expected score?