PS: GMAT-Prob

[him1985]

A contest will consist of n questions, each of which is to be answered either "True" or "False". Anyone who answer all n questions correctly will be winner. What is the least value of n for which the the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be winner?
1. 5
2. 10
3. 50
4. 100
5. 1000

Ans: B

[ronnie1985]

There are 2^n combination of answer choices of which only one is correct. Hence the probability of being right by choosing answer choices randomly is 1/2^n. To make this probability< 1/1000, we need 1/2^n<1/1000. 2^10 = 1-24>1000 = > 1/2^10<1/1000. Therefore (B) is answer.

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A contest will consist of n questions, each of which is to be answered either "True" or "False". Anyone who answer all n questions correctly will be winner. What is the least value of n for which the the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be winner?
1. 5
2. 10
3. 50
4. 100
5. 1000



For having the probability less than 1/1000, mind you the 4 options B, C, D, E are alright. But remember that in the question the least value of 'n' is asked. Hence 10 is the least among all the 4 options. Hence the correct answer comes out to be 10 i,e B.

Good probability question...


Hope this helps...