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Mammon

Probability Calculations

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*** Mod's note: Split this from another topic. - sN ***

What about the fact that there are fewer than 800 billionaires world wide?

http://money.cnn.com/2006/03/09/news/newsm...orbes/index.htm

Of those, only 371 live in the US (elsewhere, it would be far less likely that someone has ever heard of Ayn Rand or Objectivism).

How many Objectivists are there in the world? I would guess that there are fewer than ten thousand.

This needs to be looked at too. The sheer probabilty of being an Objectivist and being a Billionare is just small right now, because there are only 800 billionares and only, going off the same rough guess as Laszlo here, under 10,000. We can do some simple calculations going with these numbers,

800/6,000,000,000= 1.333333333333e-7

Very very small number, plus the probabilitiy of being an Objectivist which we will put around 10000...

10000/6,000,000,000=1.66666666666667e-7

Mmmmm.... Combine the numbers and get 3... subtract the probabilitiy of both 18,000/ 6 billion equals 3E-6...

Which subtracting the 3 we get something in the neighborhood of .0000001% of the population could be both an Objectivist and a billionare....

Edited by softwareNerd
Added split-topic annotation

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Mammon,

In addition to incorrectly adding the probabilities instead of multiplying them, your analysis has a much deeper error. You are operating on the premise that the probability of being a billionaire is completely independent of being an Objectivist. In other words, by your implicit assumption you are arguing that becoming an Objectivist offers no advantage to becoming a billionaire.

Unless if you subsequently proceed with valid hypothesis testing, this is probably not the kind of argument that you wish to make. :thumbsup:

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Are you sure?

http://www.quickmba.com/stats/probability/

Independent events are mutiplied, meaning one event doesn't affect the chances of the other. Which is why I used the Addition Law...

P(A or <_<= P(A)+ P(B) - P(A and B).

P(800/6 billion) + (10000/ 6 billion) - (18000/6 billion)

That takes both probabilities into account. Which, I was trying to find the chances are both happening at once, not the chances of one affecting the other. So I used the right equation for what I was talking about at the moment. So your right. But, I wasn't making that arguement, just trying to come up with a figure that shows how small the chances it would be too have both of these already two small chances occuring.

I didn't really do the best job at that, with my on-the-fly-math. :thumbsup:

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Independent events are mutiplied, meaning one event doesn't affect the chances of the other.
You don't have independent events. Being an Objectivist is not a property randomly distributed in the world's population, nor is being a billionaire. That should be more obvious is you consider the world's population of Registered Objectivists (100,000) and Registered Communists (1,000,000) -- the changes of being an Objectivist Communist are zero.

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P(800/6 billion) + (10000/ 6 billion) - (18000/6 billion)

Methodology aside (reluctantly, because DW is entirely correct), your arithmetic is also bad. That should have been 10800/6 billion, and....

800/6,000,000,000= 1.333333333333e-7

Very very small number, plus the probabilitiy of being an Objectivist which we will put around 10000...

10000/6,000,000,000=1.66666666666667e-7

the second number should have been e-6.

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You don't have independent events. Being an Objectivist is not a property randomly distributed in the world's population, nor is being a billionaire. That should be more obvious is you consider the world's population of Registered Objectivists (100,000) and Registered Communists (1,000,000) -- the changes of being an Objectivist Communist are zero.

*sigh*

If I don't have independent events then being a billionare and being an Objectivist are totally dependent on each other now and always, right?

AGAIN, I was just trying to get a rough number of the chances of being an Objectivist, then being a billionare, then the chances are being both of these at the same time. Not the chances of an Objectivist becoming a billionare because they are an Objectivist.

The point I was trying to make, was this...

There is a slim chance of a person being an Objectivist out of 6 billion people in the world.

There is a slim chance of a person being a billionare out of 6 billion people in the world.

There is an even slimer chance of a person being an Objectivist and a billionare at the same time.

Edit -- In which case we use the Addition law, not the Mutiplication law, because there can be Objectivists who aren't billionares and vice versa. The Mutiplication Law would assume all the billionares were, in fact, Objectivists.

Edited by Mammon

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Methodology aside (reluctantly, because DW is entirely correct), your arithmetic is also bad. That should have been 10800/6 billion, and....

the second number should have been e-6.

Both were actually typos... but I also translated the typo into my calculator! :thumbsup:

In that case it would be 3 - 1.8e-6 ... which my calculator refuses to do. <_<

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There is an even slimer chance of a person being an Objectivist and a billionare at the same time.
Unless there is some property of being an Objectivist that also causes one to do things that cause one to be a billionaire. In other words, your mistake is in not trying to compute the chances of an Objectivist becoming a billionaire because they are an Objectivist. That kind of statistical reasoning is invalid, yet common. You can't compute the "chances" of an Objectivist being a billionaire from the population frequency of billionaires and Objectivists. What you can do is do that computation and then determine what the actual frequency is, and compare the two numbers, to learn if there is something surprising about the number of Objectivist billionaires, compared to the number of socialist billionaires or Kantian billionaires.

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Unless there is some property of being an Objectivist that also causes one to do things that cause one to be a billionaire. In other words, your mistake is in not trying to compute the chances of an Objectivist becoming a billionaire because they are an Objectivist. That kind of statistical reasoning is invalid, yet common. You can't compute the "chances" of an Objectivist being a billionaire from the population frequency of billionaires and Objectivists. What you can do is do that computation and then determine what the actual frequency is, and compare the two numbers, to learn if there is something surprising about the number of Objectivist billionaires, compared to the number of socialist billionaires or Kantian billionaires.

More hairsplitting.

It's not an invalid statistical reasoning. It would be the same computation if I wanted to know the probability of someone being black and having cancer in the population.

It's the Venn Diagram on the site I linked, what of the chances of a sample being in both of the A and B circles. It only produces a number, a percentage of the population, which is what I was trying to say.

The point being that there are so few Objectivists and so few billionares out of the entire population of people on earth that the chances of someone fitting into these two categories at the same time is very very small. Which goes back to what LaszloWalrus said, which goes back to what blackdiamond.

It doesn't matter if the two things are dependent, at the moment I was assuming they are independent of each so I could give the chance of someone fitting into these two categories at the same time

Which, the point IS, that it's a matter of sheer odds as well... on top of other factors. Even if you used the number, 0.0000001% being the answer it still might be wrong, because there just might be zero.

Again, this is a rough estimate to show the rough odds to show that there is a very slim chance of someone being an Objectivist and a billionare at the same time because there are already so few of both (compared to world's over all population).

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Mammon,

What you attempted to calculate was the probability that a person is an Objectivist and a billionaire under the assumption that both attributes are independent. Unless if you are planning to do some hypothesis testing, such an estimate is utterly meaningless, especially since there is good reason to believe that these two attributes are not independent.

Would you undergo the same computation had you wanted to compute the probability that a house pet is both a dalmatian and a dog? That is, take the probability that a pet is a dog and multiply it by the probability that a pet is a dalmatian?

This is not polypyloctomy.

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Would you undergo the same computation had you wanted to compute the probability that a house pet is both a dalmatian and a dog? That is, take the probability that a pet is a dog and multiply it by the probability that a pet is a dalmatian?

Or, even better: would you say your computation method is valid for determining the likelihood that a severely mentally retarded person is a self-made billionaire? Obviously, it's not simply a question of the number of people, the number of billionaires, and the number of severely mentally retarded people.

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It's not an invalid statistical reasoning. It would be the same computation if I wanted to know the probability of someone being black and having cancer in the population.
I'm puzzled that you could so persistently fail to understand your error. It is not reasoning at all. Reasoning is the application of logic to knowledge, which produces other knowledge. Your computation does not produce knowledge, and thus it is not valid as a tool for creating knowledge. When two variables are dependent, you cannot compute the frequency of occurrence, and you cannot know anything about the frequency of occurrence of two ovents simultaneously, from the frequencies of the component events. The fact that you can multiply two numbers together shows nothing about the validity of the computation, and you should not ever offer such a meaningless computation as pointing to any fact, because it simply does not do so.

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More hairsplitting.

It's not an invalid statistical reasoning. It would be the same computation if I wanted to know the probability of someone being black and having cancer in the population.

I think you want to use conditional probability here. What is the probability of getting cancer given that one is black.

P(C|B ) = P(B&C )/P(B ). This is how you can use the joint probability

Bob Kolker

Edited by Robert J. Kolker

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Here's how to impart some methodological soundness into the question.

Consider selecting a single person at random and asking what is the probability that he is

(i) a billionaire?

(ii) an Objectivist?

(iii) a billionaire Objectivist?

How does (iii) compare to (i) times (ii)? If there is a difference, what is the cause of the difference? E.g., rounding error, data anomaly, statistically predictable anomaly, causal relationship between being an Objectivist and being a billionaire?

Of course, figuring the correlation between randomly selecting a billionaire and randomly selecting an Objectivist from the world population is a more scientific technique.

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