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by sana.noor » Mon Aug 05, 2013 11:19 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 is B
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by [email protected] » Tue Aug 06, 2013 12:28 am
Hi sana.noor,

You can can use the answers to this question to figure out the correct answer.

Since the prompt refers to "guessing randomly" and either question is either true or false, there are 2 possible results per question (you either get the question right or wrong by guessing). The prompt asks for the least number of questions that would make the probability less than 1/1000 of getting all the questions correct by guessing.

If there were 5 question, then there are 2^5 possible outcomes. This equals 1/32 which is NOT what we're looking for.
If there were 10 questions, then there are 2^10 possible outcomes. This equals 1/1024, which IS what we're looking for.

Final answer is B

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by ganeshrkamath » Tue Aug 13, 2013 12:32 am
sana.noor wrote: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 is B
The probability of winning by guessing is 1/2^n.
Now the question requires 1/2^n < 1/1000
2^n > 1000
n > 9
The least integer which satisfies the above inequality is 10.
Hence B.
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