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# A contest will contain n questions each of which is to be

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Manager
Joined: 07 Feb 2010
Posts: 136
A contest will contain n questions each of which is to be [#permalink]

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02 Nov 2010, 06:31
1
5
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Difficulty:

35% (medium)

Question Stats:

67% (01:22) correct 33% (01:28) wrong based on 205 sessions

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A contest will contain 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 then 1/1000 then a person who randomly guesses the answer to each q's will be a winner?

A. 5
B. 10
C. 50
D. 100
E. 1000
Math Expert
Joined: 02 Sep 2009
Posts: 46297
Re: a contest will contain n questions [#permalink]

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02 Nov 2010, 06:48
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1
anilnandyala wrote:
a contest will contain 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 probablity is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner?

a) 5
b) 10
c) 50
d) 100
e) 1000

The probability that a person will randomly guess all $$n$$ questions correctly is $$\frac{1}{2^n}$$, so we want the value of $$n_{min}$$ for which $$\frac{1}{2^n}<\frac{1}{1000}$$ --> $$2^n>1000$$ --> as $$n$$ is an integer $$n_{min}=10$$ ($$2^{10}=1024>1000$$).

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Manager
Joined: 06 Aug 2010
Posts: 192
Location: Boston
Re: a contest will contain n questions [#permalink]

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02 Nov 2010, 06:50
The probability of answering all the questions correctly is $$\frac{{1}}{{2^n}}$$. We want this probability to be less than $$\frac{1}{1,000}$$, so we need the smallest value of n that gives us $$2^n > 1,000$$. $$2^{10} = 1,024$$, so the answer is 10. B.
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Joined: 09 Sep 2013
Posts: 7041
Re: A contest will contain n questions each of which is to be [#permalink]

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20 Sep 2017, 21:16
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Re: A contest will contain n questions each of which is to be   [#permalink] 20 Sep 2017, 21:16
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# A contest will contain n questions each of which is to be

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