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n questions

by crackgmat007 » Fri Aug 14, 2009 8:45 pm
n questions can either be true or false. If you answer all n correct you win. What is the least value of n for which the probability is less than 1/1000 for you to win by guessing randomly?
a. 5
b. 10
c. 50
d. 100
e. 1000

OA - B
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by ashis979 » Fri Aug 14, 2009 9:04 pm
Each question has only 2 choices: true or false. And therefore, for each question you have a 50% chance of getting it correct.

So the probability of getting them all correct is:
1/2*1/2*1/2*1/2*..... you'll do this n times for n questions. Therefore, the probability of getting them all correct is (1/2)^n

From the question, we can set the following inequality:
(1/2)^n<(1/1,000) (question asks for the probability to be less than 1/1,000)
=> 2^n>1,000

When n=10, 2^10=1,024. Therefore 10 is the least value for n to win by guessing randomly. I'm assuming n has to be an integer here because you cannot have fractional questions! So B.
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