Consider a test that contains 10 multiple-choice questions with 4 possible choices for each question, only one of which is correct. Suppose a student is selected randomly. Let be the number of questions the student answers correctly. (a) Write down the distribution of . (b) Find the probability that the student did not get any answer correct. (c) The student would fail the test if he answers more than 5 questions wrongly. What is the probability that the student failed the test. (d) Find the expected number of questions the student answers correctly