Suppose that you are taking a quiz of five multiple choice questions (the instructor chose the questions randomly), with each question having four possible responses. You did not study at all for the quiz and will randomly guess which is the correct response for each question. The random variable X is the number of correct responses. a. If each question has four possible responses, why is this a valid binomial experiment?
b. State the values of n and p.
c. Calculate the probability that you will pass this quiz by correctly responding to at least three of the five questions. Is this good news for you?
d. Use your answer to part (c) to find the probability that you will not pass the quiz.