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A quiz consists of X questions, each of which is to be answered either

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Math Expert
Joined: 02 Sep 2009
Posts: 58981
A quiz consists of X questions, each of which is to be answered either  [#permalink]

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02 Oct 2018, 02:27
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:56) correct 53% (01:55) wrong based on 31 sessions

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A quiz consists of X questions, each of which is to be answered either “Yes” or “No.” One who answers all X questions correctly is a winner. What is the least value of X for which the
probability is less than 1/500 , 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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Math Expert
Joined: 02 Aug 2009
Posts: 8139
Re: A quiz consists of X questions, each of which is to be answered either  [#permalink]

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02 Oct 2018, 19:10
Bunuel wrote:
A quiz consists of X questions, each of which is to be answered either “Yes” or “No.” One who answers all X questions correctly is a winner. What is the least value of X for which the
probability is less than 1/500 , 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

Probability of answering one question right is 1/2, so answering all x correctly is 1/2*1/2*1/2...x times=1/2^x
Thus $$\frac{1}{2^x}<\frac{1}{500}............2^x>500$$
2^9 is 512>500 and 2^8 is 256<500
Thus least value of x is 9

B
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Re: A quiz consists of X questions, each of which is to be answered either   [#permalink] 02 Oct 2018, 19:10
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