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by mysseo » Mon Jan 02, 2012 10:43 pm
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 1/1,000 that a person who randomly guessing the answer to each question will be a winner?

A. 5
B. 10
C. 50
D. 100
E. 1,000
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by Anurag@Gurome » Mon Jan 02, 2012 10:58 pm
mysseo wrote: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 1/1,000 that a person who randomly guessing the answer to each question will be a winner?

A. 5
B. 10
C. 50
D. 100
E. 1,000
Probability of guessing the correct answer = 1/2
So, for N questions, the probability of guessing the correct answer = (1/2)^N
Now, (1/2)^N < 1/1000
If N = 5, then 1/32 < 1/1000 is not true.
If N = 10, then 1/1024 < 1/1000 is true.

The correct answer is B.
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by mysseo » Mon Jan 02, 2012 11:05 pm
Thank you Anurag,
"The probability of guessing the correct answer is 1/2" is the key to the solution. I couldn't think of this when I first encountered this problem.
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by Anurag@Gurome » Mon Jan 02, 2012 11:06 pm
mysseo wrote:Thank you Anurag,
"The probability of guessing the correct answer is 1/2" is the key to the solution. I couldn't think of this when I first encountered this problem.
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by ArunangsuSahu » Tue Jan 03, 2012 7:34 pm
This is a PROBABILITY Question:
1. Each question can have 2 possibilities. "TRUE" or "FALSE"

So for N questions total 2^N possibilities =Sample Space.

There is only one way all questions get corrected

so according to the question
1/2^N<1/1000

N=10

(B) is the answer
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