Probability... ah!

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Probability... ah!

by unikatrin » Tue Nov 17, 2009 7:10 pm
This is from "99 more 700+ GMAT questions" that some good soul posted on this web site.

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
(apparently, the correct answer is B)

Now, my logic is this: this is sort of like tossing a coin. You always have a 50% chance to win. Winning (i.e., guessing right) on N questions would then be 1/2 times 1/2 times 1/2... or (1/2)^N (1/2 to the power of N).

2^14 is 512; 2^15 is 1024. So, your probability to win if you have 14 questions is 1/512>1/1000. Probability to win if you have 15 questions is 1/1024<1/1000. So the correct answer to this question would have to be N>14; of the answer choices above, it would be C, 50.

Thoughts/ideas? Any tips are much appreciated! I'm less than a week away from GMAT, and probability/permutations is definitely my weak link. Thanks, guys!
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by Stuart@KaplanGMAT » Tue Nov 17, 2009 7:41 pm
unikatrin wrote:This is from "99 more 700+ GMAT questions" that some good soul posted on this web site.

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
(apparently, the correct answer is B)

Now, my logic is this: this is sort of like tossing a coin. You always have a 50% chance to win. Winning (i.e., guessing right) on N questions would then be 1/2 times 1/2 times 1/2... or (1/2)^N (1/2 to the power of N).

2^14 is 512; 2^15 is 1024. So, your probability to win if you have 14 questions is 1/512>1/1000. Probability to win if you have 15 questions is 1/1024<1/1000. So the correct answer to this question would have to be N>14; of the answer choices above, it would be C, 50.

Thoughts/ideas? Any tips are much appreciated! I'm less than a week away from GMAT, and probability/permutations is definitely my weak link. Thanks, guys!
Your reasoning is perfect; your math, not so much!

2^10 = 1024, not 2^15.
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by unikatrin » Wed Nov 18, 2009 4:41 am
Whoops. Not sure what I was thinking... must have been tired last night. Thanks!

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by sreak1089 » Wed Nov 18, 2009 7:09 am
So the answer should be B isn't it?

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by unikatrin » Wed Nov 18, 2009 7:16 am
Yup. Hope I don't make mistakes like that on the actual GMAT!!! That's embarrassing. :-)

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by vineetbatra » Fri Jan 29, 2010 6:27 am
If N is ten then the probability of winning will be 1/1024, which is the least value smaller than 1/1000.

1/1000> 1/1024.

Please let me know if my understanding is correct.