Richard has been given 7-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. Supposing that Richard guesses on all 7 questions, determine the probability that he will answer at least six questions correctly? Round your answer to the nearest thousandth.
Answer
a. 0.857
b. 0.006
c. 0.007
d. 0.500
e. 0.286