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# A contest will consist of n questions, each of which is to

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VP
Joined: 22 Nov 2007
Posts: 1063
A contest will consist of n questions, each of which is to  [#permalink]

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27 Dec 2007, 09:28
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Difficulty:

15% (low)

Question Stats:

79% (00:45) correct 21% (01:14) wrong based on 253 sessions

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A contest will consist of 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 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contest-will-consist-of-n-questions-each-of-which-is-to-38710.html
Director
Joined: 12 Jul 2007
Posts: 853
Re: A contest will consist of n questions, each of which is to  [#permalink]

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27 Dec 2007, 10:37
1
Each question has 2 ways to guess so the probability of guessing correctly is 1/2. The probability of guessing each question correctly for n questions is 1/2^n. What is the smallest number for n that gets the denominator over 1000?

1/2^n = probability

1/2^5 = 1/32
1/2^10 = 1/1024

and you don't need to go any further. Someone guessing on 10 questions has a 1/1024 chance of getting them all correct.

Manager
Joined: 27 Oct 2008
Posts: 180
Re: A contest will consist of n questions, each of which is to  [#permalink]

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27 Sep 2009, 11:29
A contest will consist of 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 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

Soln: ans is B

Probability that one question is answered right is 1/2.

Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/1000
n = 10 satisfies this.
VP
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Re: A contest will consist of n questions, each of which is to  [#permalink]

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02 May 2011, 09:41
1/2^n < 1/1000

n= 10 is the least value of number of questions. 1/2 is for equal probability of true and false.
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Math Expert
Joined: 02 Sep 2009
Posts: 47923
Re: A contest will consist of n questions, each of which is to  [#permalink]

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10 Dec 2014, 03:45
1
4
A contest will consist of 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 than 1/1000 that a person who randomly guesses the answer to each question will be 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 $$\frac{1}{2^n}<\frac{1}{1,000}$$ --> $$2^n>1,000$$ --> $$n_{min}=10$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contest-will-consist-of-n-questions-each-of-which-is-to-38710.html
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Posts: 7719
Re: A contest will consist of n questions, each of which is to  [#permalink]

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24 Jul 2018, 08:37
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Re: A contest will consist of n questions, each of which is to &nbs [#permalink] 24 Jul 2018, 08:37
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