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.

Accepted Solution

The probability is 1/729.

To advance to the 7th round, the contestant must guess 6 answers correctly.Β  There is a 1/3 chance of this, since there are 3 choices with 1 correct.Β  This gives us

(1/3)^6 = (1^6)/(3^6) = 1/729