Richard has been given a 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. Assuming that Richard guesses on all 7 questions, find the probability that he will answer at least 6 questions correctly. Round your answer to the nearest thousandth.
A)0.006
B)0.007
C)0.857
D)0.286
E)0.500

Question

Quizplus · Accepted Answer

The probability of guessing one question correctly is 1/3, and the probability of guessing one question incorrectly is 2/3. Using the binomial probability formula, we can find the probability of answering at least 6 questions correctly as follows:

P(X ≥ 6) = P(X = 6) + P(X = 7)
= (7C6)(1/3)^6(2/3)^1 + (7C7)(1/3)^7(2/3)^0
= 0.00694 + 0.00098
= 0.00792

Rounding to the nearest thousandth gives us 0.007, which is answer choice B.

Richard Has Been Given a 7-Question Multiple-Choice Quiz in His