Quiz-

MURALIDHARGAJULA wrote:In a quiz, the contestant is asked 10 questions, to which he should answer true or false. He should answer at least 8 questions correctly to move on to the next level of the quiz. If he answers all the questions, what is the probability that he does not proceed to the next level?

He will move to the next level if any one of the following scenarios,

• 1. He answers exactly 8 questions correctly.
  2. He answers exactly 9 questions correctly.
  3. He answers all the 10 questions correctly.

Exactly 8 questions out of 10 can be answered correctly in 10C8 = 45 ways
Exactly 9 questions out of 10 can be answered correctly in 10C9 = 10 ways
All the 10 questions can be answered correctly in 10C10 = 1 way
Hence, he can move to the next level in (45 + 10 + 1) = 56 ways

Now, total number of ways he can answer 10 questions = 2^10 = 1024

Hence, probability that he proceeds to the next level = 56/1024 = 7/128
Hence, probability that he does not proceed to the next level = (1 - 7/128) = 121/128

The correct answer is C.