Richard has been given a 10-question multiple-choice quiz in his history class. Each question has three 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 10 questions, find the probability that he will answer at least 6 questions correctly. Round your answer to the nearest thousandth.
A)0.057
B)0.500
C)0.600
D)0.200
E)0.077

Question

Quizplus · Accepted Answer

The probability of guessing a question correctly is 1/3, and incorrectly is 2/3. Using the binomial probability formula, the probability of getting at least 6 correct answers out of 10 is calculated as P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10). This results in approximately 0.077.

Richard Has Been Given a 10-Question Multiple-Choice Quiz in His