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# Gmatprep - probability

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Gmatprep - probability [#permalink]  08 Feb 2007, 20:56
OA: B
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From the question: there are n questions and the contestant can only answer yes or no.

Prob[answer all questions correctly] = (possible ways to answer all n question correct)/(possible ways to answer the question randomly)

Count Possible ways to answer all n question correctly = 1 x 1 x 1 x ... x 1 (n times) = 1^n = 1

Count Possible ways to answer question randomly = 2 x 2 x 2 x 2 x ... x 2 (n times) = 2^n

Prob = 1/(2^n)

Now Prob < 1/1000

1/(2^n) < 1/1000

n could be 10, 11, 12, 13, ... , oo

the least value of n so that; 1/2^n < 1/1000.

n = 10.

Last edited by devilmirror on 08 Feb 2007, 21:18, edited 1 time in total.
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Or, you can use another method.

There are n questions. The chance of answering each question correctly = 0.5 = 1/2 {Because you can only answer True o False}

Chance of answering all n question correctly = (0.5) x (0.5) x ... x (0.5) = 0.5^n

0.5^n < 1/1000

n can only be 10.
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Re: Gmatprep - probability [#permalink]  08 Feb 2007, 23:21
joyce wrote:
OA: B

This is like flipping a coin

You can answer a question either true or false hence the prob of answering each question correctly is 0.5

Therefore probability of answering n questions correct is (0.5)^n

Now it is said that (0.5)^n < 1/1000

giving n as 10 the answer
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Re: Gmatprep - probability   [#permalink] 08 Feb 2007, 23:21
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