Question 6.155

57. Random Guessing on a Quiz. 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 the correct response for each question. The random variable is the number of correct responses.

  1. If each question has four possible responses, why is this a valid binomial experiment?
  2. State the values of and .
  3. 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?
  4. Use your answer to (c) to find the probability that you will not pass the quiz.

6.2.57

(a) It fulfills the requirements: (i) There are only two possible outcomes for each trial: correct answer or incorrect answer. (ii) We know in advance that the quiz will have 5 questions. (iii) Since you are randomly guessing the answer to each question, the trials are independent. (iv) Since each question has 4 responses, the probability of guessing correctly remains the same from question to question. (b) , (c) 0.1035 (d) 0.8965