Probability Query

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sinha: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Apr 22, 2011 7:27 am

by sinha » Thu Jun 30, 2011 10:25 am

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

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Source: Beat The GMAT — Problem Solving | Thu Jun 30, 2011 10:25 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jun 30, 2011 10:40 am

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.

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

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treker: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Fri Aug 22, 2008 9:32 pm; Thanked: 1 times

by treker » Thu Jun 30, 2011 7:11 pm

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"

Thanks!
- Treker

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jun 30, 2011 8:29 pm

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.

Cheers!

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

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Thu Jun 30, 2011 9:18 pm

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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