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Probability Q

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Junior | Next Rank: 30 Posts
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by mrkylee » Tue Oct 23, 2007 7:03 pm
a contest will consist of n questions, each of which is to be answered either "true" of "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?

The ans is 10, but I can't seem to solve. Please help.
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by jangojess » Tue Oct 23, 2007 8:49 pm
prob of getting an ans right/wrong = 1/2
so the prob of getting all the ans right = (1/2)^n, which as per the Q shld be less than 1/1000
1/2^n < 1/1000 ==> 2^n > 1000 and we need to find the least value of n which satisfies the cond...and that value is 10 (2^10 = 1024)
Trying hard!!!
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