Que: A quiz consists of X questions, each of which is to be answered either “Yes” or “No.” What is the least value....

Solution: Total questions: X

Total options for each question: 2 [Yes or No]

Thus, the probability of randomly guessing an answer and getting it correct = \(\frac{1}{2}\)

Thus, the probability of randomly guessing answers to all X questions and getting them correct:

=> \(\frac{1}{2}\) * \(\frac{1}{2}\) * ….. X times

=> \(\left(\frac{1}{2}\right)^x\)

=> \(\left(\frac{1}{2}\right)^x\ <\frac{1}{500}\)

=> \(\left(\frac{1}{2^x}\right)\ <\frac{1}{500}\)

=> \(2^x>500\)

For x = 9, \(2^9=512\), which just exceeds 500.

Therefore, B is the correct answer.

Answer B