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# PS: Probability contest

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Senior Manager
Joined: 18 Jun 2007
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PS: Probability contest [#permalink]  21 Sep 2008, 11:49
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A contest will consist of n questions and each question to be answered either ‘true’ or ‘false’. Anyone who answers all questions correctly will be the 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 the winner?
A. 5
B. 10
C. 50
D. 100
E. 1000

Manager
Joined: 28 Aug 2008
Posts: 102
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Re: PS: Probability contest [#permalink]  21 Sep 2008, 12:37
B

IF 10 questions, prob of getting all 10 right is .00097, which is less than .001
VP
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Re: PS: Probability contest [#permalink]  21 Sep 2008, 21:41
rishi2377 wrote:
A contest will consist of n questions and each question to be answered either ‘true’ or ‘false’. Anyone who answers all questions correctly will be the 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 the winner?
A. 5
B. 10
C. 50
D. 100
E. 1000

Probability of answering a Question right = 1/2

N Questions is 1/2 X 1/2 X 1/2 ... n times means (1/2) ^ n

We need to find least n such that (1/2) ^ n < 1/1000

If n =5 1/32 > 1/1000

n =10 1/1024 < 1/1000

Hence B
Re: PS: Probability contest   [#permalink] 21 Sep 2008, 21:41
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