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A contest will consist of n questions, each of which is to

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A contest will consist of n questions, each of which is to [#permalink]

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New post 27 Dec 2007, 09:28
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A contest will consist of n questions, each of which is to be answered either "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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contest-will-consist-of-n-questions-each-of-which-is-to-38710.html
[Reveal] Spoiler: OA

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Re: A contest will consist of n questions, each of which is to [#permalink]

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New post 27 Dec 2007, 10:37
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Each question has 2 ways to guess so the probability of guessing correctly is 1/2. The probability of guessing each question correctly for n questions is 1/2^n. What is the smallest number for n that gets the denominator over 1000?

1/2^n = probability

1/2^5 = 1/32
1/2^10 = 1/1024

and you don't need to go any further. Someone guessing on 10 questions has a 1/1024 chance of getting them all correct.

Answer: B

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Re: A contest will consist of n questions, each of which is to [#permalink]

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New post 27 Sep 2009, 11:29
A contest will consist of n questions, each of which is to be answered either "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

Soln: ans is B

Probability that one question is answered right is 1/2.

Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/1000
n = 10 satisfies this.

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Re: A contest will consist of n questions, each of which is to [#permalink]

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New post 02 May 2011, 09:41
1/2^n < 1/1000

n= 10 is the least value of number of questions. 1/2 is for equal probability of true and false.
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Re: A contest will consist of n questions, each of which is to [#permalink]

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New post 09 Dec 2014, 21:58
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Re: A contest will consist of n questions, each of which is to [#permalink]

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New post 10 Dec 2014, 03:45
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A contest will consist of n questions, each of which is to be answered either "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 winner?

A. 5
B. 10
C. 50
D. 100
E. 1000

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contest-will-consist-of-n-questions-each-of-which-is-to-38710.html
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Re: A contest will consist of n questions, each of which is to   [#permalink] 10 Dec 2014, 03:45
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