Problem
In each round of a game show, a contestant answers a multiple-choice question that has three answer choices. The contestant advances to the next round by answering the question correctly. What is the probability of advancing to the seventh round if the contestant randomly guesses the answer to each question? Write your answer as a fraction in simplest form. The probability of advancing to the seventh round is
Solution
Step 1 ：The probability of guessing the correct answer for each question is \(\frac{1}{3}\)
Step 2 ：The probability of advancing to the seventh round is the product of the probabilities for each question: \(\left(\frac{1}{3}\right)^6 = \boxed{\frac{729}{729000000}}\)
