A student takes a multiple-choice quiz consisting of five problems, each with four possible answers, only one of which is correct. Suppose that the student guesses randomly on each question. Let be the number of questions the student answers correctly. Notice that is a binomial random variable.

a) Identify and in this situation. (2 pts)

b) Complete the table below, showing the probability distribution of . (4 pts)

c) Find the probability that the student gets at most three problems correct. (2 pts)

d) Find the probability that the student gets at least three problems correct. (2 pts)

e) What is the probability that the student gets any one particular problem incorrect? (1 pt) f) What is the probability that the student gets the first problem correct and the second incorrect? (2 pts)

g) What is the average number of problems the student will get correct in this situation? (2 pts)