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Probability aptitude questions‏?
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cardguy Offline
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Post: #1
Probability aptitude questions‏?
Hey everyone,

Just got this email from a close friend of mine. Just wanted to see if I could take advantage of the combined brain power here on the forum to help him out. Cheers!

Quote:Hi guys,

I have an interview coming up which will ask me a lot of statistical/probability aptitude questions.

However, unfortunately the ones I could find on the internet are not difficult enough to help me properly prepare. I know there are documents out there which have loads of these to enable people to practice for such interviews. And, i was hoping that someone in my highly skilled circle of friends would have such a document, or could tell me where I could get it.

The questions will all be probability questions designed to see how clever someone is, and are of the type:

"If there is a 50% probability of stars in one night, what is the probability of stars in either of two nights?"

I would greatly appreciate your help on this if you have access to such a document. If not, I hope all is going well with you.

Cardguy
06-06-2013 05:31 AM
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cibo Offline
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RE: Probability aptitude questions‏?
If I'm not misreading the question.

75%

Probably of not having a starry night. Order does not matter. 50% not starry x 50% not starry= 25% Therefore 75% chance of at least one or more of the nights being starry.

Also it can be thought of as a permutation.
S NS
NS S
S S
NS NS

3/4 don't.

If it means Starry given a previous condition P(Night Sky|Night Sky-1), it's still 50%
(This post was last modified: 06-06-2013 11:05 AM by cibo.)
06-06-2013 11:04 AM
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lurker Offline
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RE: Probability aptitude questions‏?
Whenever you're asked to find the probability of something occurring at least once through a set of events with defined probability, the easiest way to do it is to calculate the probability that it never happens and subtract that from 1.

The probability it never happens is the product of all the individual probability events that it doesn't occur. Here, there's a 50% chance any one night is starry, which means there's a 50% chance any one night is not starry. Thus, the probability that both nights are not starry is 0.5 * 0.5 = 0.25. This means the probability that at least one night is starry is 1-0.25 = 0.75.

Likewise, the probability of at least one night in three being starry would be 1- (0.5*0.5*0.5) = 1-0.125 = 0.875.

If he needs to know the probability of exactly X number of nights being starry out of N total, he needs to use the binomial distribution.
06-06-2013 11:16 AM
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TheKantian Offline
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RE: Probability aptitude questions‏?
If he needs to know legit probability, then he'll probably need a book.
06-06-2013 11:36 AM
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Soma Away
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RE: Probability aptitude questions‏?
The book Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller might be what he's looking for. I have a .djvu copy if you want it.

I can't have sex with your personality, and I can't put my penis in your college degree, and I can't shove my fist in your childhood dreams, so why are you sharing all this information with me?
06-06-2013 12:32 PM
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Hades Offline
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RE: Probability aptitude questions‏?
Might want to brush up on set theory in the meantime so you are completely sure what the mathematical definitions for "either", "or", "and", and similar words are.
06-06-2013 01:16 PM
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ElBorrachoInfamoso Away
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RE: Probability aptitude questions‏?
Has he checked MIT OCW?

He might find good problems if he looks through the course materials they post.

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06-06-2013 01:21 PM
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SpiderKing Offline
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RE: Probability aptitude questions‏?
(06-06-2013 12:32 PM)Soma Wrote:  The book Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller might be what he's looking for. I have a .djvu copy if you want it.


Soma,

Could I please get a copy? I have a possible interview coming up which will require knowledge of probabilities. Thanks.


Regards,
SK

"The whole point of being alpha, is doing what the fuck you want.
That's why you see real life alphas without chicks. He's doing him.

Real alphas don't tend to have game. They don't tend to care about the emotional lives of the people around them."

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06-06-2013 01:23 PM
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cardguy Offline
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RE: Probability aptitude questions‏?
(06-06-2013 12:32 PM)Soma Wrote:  The book Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller might be what he's looking for. I have a .djvu copy if you want it.

Cheers! Just PM'ed you.
06-06-2013 02:08 PM
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Divorco Offline
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RE: Probability aptitude questions‏?
06-06-2013 02:18 PM
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RE: Probability aptitude questions‏?
(06-06-2013 02:18 PM)Divorco Wrote:  Heard on the Street: Quantitative Questions from Wall Street Job Interviews

I also have a .djvu copy of this.

I can't have sex with your personality, and I can't put my penis in your college degree, and I can't shove my fist in your childhood dreams, so why are you sharing all this information with me?
06-06-2013 03:11 PM
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LeBeau Offline
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RE: Probability aptitude questions‏?
(06-06-2013 11:16 AM)lurker Wrote:  Whenever you're asked to find the probability of something occurring at least once through a set of events with defined probability, the easiest way to do it is to calculate the probability that it never happens and subtract that from 1.

The probability it never happens is the product of all the individual probability events that it doesn't occur. Here, there's a 50% chance any one night is starry, which means there's a 50% chance any one night is not starry. Thus, the probability that both nights are not starry is 0.5 * 0.5 = 0.25. This means the probability that at least one night is starry is 1-0.25 = 0.75.

Likewise, the probability of at least one night in three being starry would be 1- (0.5*0.5*0.5) = 1-0.125 = 0.875.

If he needs to know the probability of exactly X number of nights being starry out of N total, he needs to use the binomial distribution.

This. The other guiding rule here is that for 2 INDEPENDENT events, in order to get the probability that they both happen, you multiply the probabilities together.

Not to confuse the issue, but where this often breaks down is in the real world where it's much harder to measure the degree of dependence (i.e. wind currents on cloud cover, condensation, light pollution, etc.)

Which also spills into an oversimplified understanding of risks and probability in society (see the writings of Benoit Mandelbrot and Nassim Taleb).
06-07-2013 12:46 AM
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