Richard has been given a 12-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 12 questions, find the probability that he will answer no more than 3 questions correctly. Round your answer to the nearest thousandth.
A)0.258
B)0.500
C)0.250
D)0.649
E)0.063

Question

Quizplus · Accepted Answer

The probability of success on each question is 1/4, since there are four possible answers and only one is correct. The probability of failure on each question is 3/4, since there are three incorrect answers. We can use the binomial distribution to find the probability of answering no more than 3 questions correctly when guessing on all 12 questions.

P(X ≤ 3) = ΣC(12, x) (1/4)^x (3/4)^(12-x) from x = 0 to x = 3

Using a calculator or software, we find that P(X ≤ 3) ≈ 0.649, which rounded to the nearest thousandth is 0.649. Therefore, the answer is D.

Richard Has Been Given a 12-Question Multiple-Choice Quiz in His