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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 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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New post 21 Feb 2012, 11:25
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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]

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New post 21 Feb 2012, 11:54
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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.

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 10 Jan 2014, 10:54
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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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New post 30 Oct 2014, 22:40
(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

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

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Re: A contest will consist of n questions, each of which is to   [#permalink] 04 May 2016, 12:08
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