Answer: [tex]\frac{1}{729}[/tex]
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 :-
[tex]\text{P(guessing the right answer)}=\frac{1}{3}[/tex]
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 :-
[tex]\text{P(Advancing seventh round )}=(\frac{1}{3})^6=\frac{1^6}{36}=\frac{1}{729}[/tex]
