Question

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.

Answer 1

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Answer 2

Answer:  $\frac{1}{729}$

Step-by-step explanation:

Given: The number of choices in in each question =3

Therefore, the probability of guessing the right answer is given by :-

$\text{P(guessing the right answer)}=\frac{1}{3}$

Since, the probability of advancing to the seventh round is product of probability of answering correctly in all the preceding rounds i.e in previous 6 rounds.

Therefore, the probability of advancing to the seventh round if the contestant randomly guesses the answer to each question is given by :-

$\text{P(Advancing seventh round )}=(\frac{1}{3})^6=\frac{1^6}{36}=\frac{1}{729}$