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A contest will consist of n questions, each of which is to be answered with "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
A. 5
B. 10
C. 50
D. 100
E. 1000
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21 Feb 2012, 11:25
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SimaQ
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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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
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
