Richard has been given a 7-question multiple-choice quiz in his history class. Each and every question has three answers, of which only one is correct. Since Richard hasn't attended the class recently, he doesn't know any of the answers. Supposing that Richard guesses on all 7 questions, find 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