Que: A quiz consists of X questions, each of which is to be answered .....

[Max@Math Revolution]

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

[Max@Math Revolution]

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