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GRE Prep Club Team Member
Joined: 20 Feb 2017
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A contest will consist of n questions, each of which is to be answered
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12 Dec 2022, 06:10
12 Dec 2022, 06:10
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A contest will consist of n questions, each of which is to be answered with "True" or "False". Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A. 5
B. 10
C. 50
D. 100
E. 1000
A. 5
B. 10
C. 50
D. 100
E. 1000
Re: A contest will consist of n questions, each of which is to be answered
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14 Dec 2022, 04:34
14 Dec 2022, 04:34
1
Expert Reply
The probability to randomly guess the answer for 1 question is 1/2, for 2 questions 1/2*1/2=1/2^2, similarly for n questions the probability is 1/2^n.
We need to find the least value of \(n\) for which \(\frac{1}{2^n}<\frac{1}{1,000}\) --> \(2^n>1,000\) --> \(n_{min}=10\).
Answer: B.
We need to find the least value of \(n\) for which \(\frac{1}{2^n}<\frac{1}{1,000}\) --> \(2^n>1,000\) --> \(n_{min}=10\).
Answer: B.
gmatclubot
Re: A contest will consist of n questions, each of which is to be answered [#permalink]
14 Dec 2022, 04:34
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