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

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

by Max@Math Revolution » Fri Jan 15, 2021 2:13 am
Que: A quiz consists of X questions, each of which is to be answered either “Yes” or “No.” What is the least value of X for which the probability is less than \(\frac{1}{500}\) such that a participant who randomly guesses the answer to each question will be a winner?

(A) 8
(B) 9
(C) 10
(D) 200
(E) 500
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Re: Que: A quiz consists of X questions, each of which is to be answered either “Yes” or “No.” What is the least value..

by Max@Math Revolution » Wed Jan 20, 2021 6:09 am
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
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