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        riddles >> general problem-solving / chatting / whatever >> Need help with probabilties
        
(Message started by: Leon on Jun 20th, 2004, 9:39am)
Title: Need help with probabilties
Post by Leon on Jun 20th, 2004, 9:39am
I was told the following:

A and B are both attempting to guess a random whole number from 1 to 10.

To get a guess, A rolls a 20 sided die with 1 - 10 on it (each number is repeated twice). To get a guess, B calls a friend who uses a highly scientific method called Q.

Who is going to get the number more often?

I have been told that B will correctly guess the number more often (10 times more often actually).

The reason being that A has a 1/10 chance with the die of getting the number which was randomly selected with a 1/10 chance. So the probability is 1%.

On the other hand, B has been given the number so only has to deal with the 1/10 chacne that that is the number. So the probability is 10%.

Is this correct?
Title: Re: Need help with probabilties
Post by towr on Jun 20th, 2004, 10:29am
no.. that's not correct.

A has 1/10th chance of guessing the number which was selected, period. How that number was selected doesn't matter.

And if B has been given the number, I don't see why he doesn't get 100% ?!?
Title: Re: Need help with probabilties
Post by Leon on Jun 20th, 2004, 12:15pm

on 06/20/04 at 10:29:24, towr wrote:
no.. that's not correct.

A has 1/10th chance of guessing the number which was selected, period. How that number was selected doesn't matter.


Good. That's what I thought. The only question is did I interpret it wrong. Is the way I stated it different from what I read? The passage reads:

"Assuming the stock maret is random....George selects one of the ten stocks by rolling a die... Martha believes in some wacky theory… dictated by a Q analysis newsletter that selects one stock of the ten as most likely to break out. Although George and Martha are equally likely to pick the lucky stock each week, the newsletter-selected stock will result in big investor gains more frequently than will any other stock.

The reason is simple but easy to miss. Two conditions must be met for a stock to result in big gains for an investor: It must be smiled upon by chance that week and must be chosen by Martha or George. Since Martha always picks the newsletter-selected stock, the second condition in her case is always met, so whenever chance happens to favor it, it results in big gains for her. This is not the case with the other stocks. Nine-tenths of the time, chance will smile on one of the stocks that is not newsletter-selected, but chances are George will not have picked that particular one, and so it will seldom result in big gains for him. One must be careful in interpreting this, however. George and Martha have equal chances of pulling down big gains (10 percent), and each stock of the ten has an equal chance of being smiled upon by chance (10 percent), but the newsletter-selected stock will achieve big gains much more often than the randomly selected ones.

Reiterated more numerically, the claim is that 10 percent of the time the newsletter-selected stock will achieve big gains for Martha, whereas each of the ten stocks has only a 1 percent chance of both achieving big gains and being chosen George."

I know it is long and I appreciate your help.
Title: Re: Need help with probabilties
Post by Leonid Broukhis on Jun 20th, 2004, 1:42pm
As the newsletter is received by other people as well that are more likely to pick the suggested stock than to make a random selection, the newsletter effectively publishes a self-fulfilling prophecy. This has nothing to do with probabilities, and all probabilities-like handwaving that is done to detract the reader's attention from that fack is just that - handwaving.
Title: Re: Need help with probabilties
Post by towr on Jun 20th, 2004, 1:47pm

on 06/20/04 at 12:15:06, Leon wrote:
"Reiterated more numerically, the claim is that 10 percent of the time the newsletter-selected stock will achieve big gains for Martha, whereas each of the ten stocks has only a 1 percent chance of both achieving big gains and being chosen George."
What they're missing here is that George get's 1% on all 10 stocks, while Martha get's 10% on one stock, and 0% on the other 9. So in the end they both get 10%..
Title: Re: Need help with probabilties
Post by Leon on Jun 21st, 2004, 11:49am

on 06/20/04 at 13:47:17, towr wrote:
What they're missing here is that George get's 1% on all 10 stocks, while Martha get's 10% on one stock, and 0% on the other 9. So in the end they both get 10%..

Not sure I follow that, but my thoughts are:

towr, the 10% is not the return, just the chance that that particular stock will gain big (by an unknown amount).

Also, isn't that similar to the statement in the passage that says "Nine-tenths of the time, chance will smile on one of the stocks that is not newsletter-selected, but chances are George will not have picked that particular one, and so it will seldom result in big gains for him."?



My contention, that it looks like y'all agree with, is that it doesn't matter how you pick the stock. Once you picked it, you have a 10% chance to be the gainer. This can be shown by asking what if Q analysis was to roll the same die? Then they'd be exactly the same since it makes no difference if someone else rolled the die and told you the # or if you roll it yourself.

If anyone is interested, here is the bio of the PhD in Math author

http://www.math.temple.edu/~paulos/

Thanks again towr and Leonid.
Title: Re: Need help with probabilties
Post by towr on Jun 21st, 2004, 12:02pm

on 06/21/04 at 11:49:13, Leon wrote:
towr, the 10% is not the return, just the chance that that particular stock will gain big (by an unknown amount).
That doesn't matter, if you want multiply by X (the unknown amount) to get the expected gain.

The only time it'll make a difference is if the gain for each stock isn't the same (in which case you should always gamble for the one which would give the biggest pay off, assuming each one is really equally likely to go up)
Title: Re: Need help with probabilties
Post by Leon on Jun 21st, 2004, 1:16pm

on 06/21/04 at 12:02:18, towr wrote:
That doesn't matter, if you want multiply by X (the unknown amount) to get the expected gain.

The only time it'll make a difference is if the gain for each stock isn't the same (in which case you should always gamble for the one which would give the biggest pay off, assuming each one is really equally likely to go up)


Gotcha. Thanks.


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