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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] New post 18 Nov 2006, 08:48
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A contest will consist of n questions, each of which is to be answered wither "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
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Re: A contest will consist of n questions, each of which is to [#permalink] New post 21 Feb 2012, 10:25
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SimaQ wrote:
A contest will consist of n questions, each of which is to be answered wither "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


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.
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Re: A contest will consist of n questions, each of which is to [#permalink] New post 21 Feb 2012, 10:54
+1 B

The probability of answering right randomly is 1/2.

So, the probability of winning the contest is \frac{1}{2} * \frac{1}{2} *....\frac{1}{2} = \frac{1}{2^n}

2^9 = 512
2^(10) = 1024

So, n must be at least 10.

ANSWER B
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Re: A contest will consist of n questions, each of which is to [#permalink] New post 10 Jan 2014, 09:54
SimaQ wrote:
A contest will consist of n questions, each of which is to be answered wither "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


Min 'n' for 2^n >=1000

2^9 = 512

Then 2^10 >=1000 actually 1024

So B
Re: A contest will consist of n questions, each of which is to   [#permalink] 10 Jan 2014, 09:54
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