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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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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
[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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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 $$\frac{1}{2^n}<\frac{1}{1,000}$$ --> $$2^n>1,000$$ --> $$n_{min}=10$$.

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

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21 Feb 2012, 10:54
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+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.

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

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10 Jan 2014, 09:54
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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

Min 'n' for 2^n >=1000

2^9 = 512

Then 2^10 >=1000 actually 1024

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

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30 Oct 2014, 21:40
(1/2)^n < 1/1000
(1/2)^n < (1/2)^3*(1/5)^3
Because 1/5 ~ (1/2)^2
n > 3 + 3*2 = 9

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

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04 May 2016, 11:08
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Re: A contest will consist of n questions, each of which is to   [#permalink] 04 May 2016, 11:08
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