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Probability Query

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Probability Query

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Can someone help me understand this question :

n question are either true or false. What is the minimum value of n for which (p) of all true <1/1000?

thanx Smile

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Hi,
Probability that each each question is correct is 1/2.
So, probability of gettign all 'n' questions correct is (1/2)^n
So, (1/2)^n < 1/1000 => 2^n > 1000
2^10 = 1024
So, n >= 10
Minimum value of n is 10.

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Last edited by Frankenstein on Thu Jun 30, 2011 8:33 pm; edited 1 time in total

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Frankenstein wrote:
Hi,
Probability that each each question is correct is 1/2.
So, probability of gettign all 'n' questions correct is (1/2)^n
So, (1/2)^n < 1000 => 2^n > 1000
2^10 = 1024
So, n >= 10
Minimum value of n is 10.
Can you please explain this stmt - "So, (1/2)^n < 1000 => 2^n > 1000"

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- Treker

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treker wrote:
Frankenstein wrote:
Hi,
Probability that each each question is correct is 1/2.
So, probability of gettign all 'n' questions correct is (1/2)^n
So, (1/2)^n < 1000 => 2^n > 1000
2^10 = 1024
So, n >= 10
Minimum value of n is 10.
Can you please explain this stmt - "So, (1/2)^n < 1000 => 2^n > 1000"
Hi,
That was a typo. I have edited now. If you are interested in the underlying principle,
If a and b are positive and a > b, then 1/a < 1/b.
Example: 3>2 .. 1/3 < 1/2.

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Things are not what they appear to be... nor are they otherwise

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probability of having a right or wrong in question = 1/2

thus 1/2^n < 1/1000 is what being asked here.

hence 2^n = 1024 is sufficient meaning n = 10.

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