Question: A student decides to randomly guess the answers to a ten question multiple choice exam. Suppose each question has four answer choices exactly one of which is correct. Given this, find the following probabilities.

a) That the student answers exactly three questions correctly.

b) That the student answers at most three questions correctly.

c) That the student answers at least four questions correctly.

d) What are the mean number of correct answers if students randomly guess in tests of this type? What are the variance and standard deviation?