Que: A quiz consists of X questions, each of which is to be answered either “Yes”, “No.” or “Don’t know.” What is the least value of X for which the probability is less than 1/300 such that a participant who randomly guesses the answer to each question will be a winner?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Que: A quiz consists of X questions, each of which is to be answered .....
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- Max@Math Revolution
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Solution: Total questions: X
Total options for each question: 3 [Yes, No, or Don’t know]
Thus, the probability of randomly guessing an answer and getting it correct = 1/3
Thus, the probability of randomly guessing answers to all X questions and getting them correct:
=> \(\frac{1}{3}\cdot\frac{1}{3}\cdot....\cdot N\ times\)
=> \(\left(\frac{1}{3}\right)^x\)
=> \(\left(\frac{1}{3}\right)^x<\frac{1}{300}\)
=> \(\left(\frac{1}{3^x}\right)<\frac{1}{300}\)
=> \(3^x>300\)
For x = 6, 36 = 729, which exceeds 300.
Therefore, C is the correct answer.
Answer C
Total options for each question: 3 [Yes, No, or Don’t know]
Thus, the probability of randomly guessing an answer and getting it correct = 1/3
Thus, the probability of randomly guessing answers to all X questions and getting them correct:
=> \(\frac{1}{3}\cdot\frac{1}{3}\cdot....\cdot N\ times\)
=> \(\left(\frac{1}{3}\right)^x\)
=> \(\left(\frac{1}{3}\right)^x<\frac{1}{300}\)
=> \(\left(\frac{1}{3^x}\right)<\frac{1}{300}\)
=> \(3^x>300\)
For x = 6, 36 = 729, which exceeds 300.
Therefore, C is the correct answer.
Answer C
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