Multiple Choice Quiz: Richard has just been given a 12-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Richard doesn't know any of the answers because he has not attended class recently. Since there are five possible answers to each question and only one of them is correct, the probability that Richard will guess the correct answer in any given question is =0.20 . Assuming that Richard guesses on all 12 questions, find the following probabilities:

a. W hat is the probability that he will answer all questions correctly? (10 points)

b. What is the probability that he will answer all questions incorrectly? (10 points)

What is the probability that he will answer 8 or more questions correctly? (10 points)

d What is the probability that he will answer 2 or less questions correctly? ( 10 points) e . What is the expected number of questions that he will answer correctly? ( 10 points)