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VP
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A contest will consist of n questions, each of which is to [#permalink]
 27 Dec 2007, 09:28
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66% (01:46) correct
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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
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Director
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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.
Answer: B
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Manager
Joined: 27 Oct 2008
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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
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.
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VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
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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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