puzzles and riddles

[jean-luc]

Oh, the letter "E".

[sushi]

Well, ALL-POWERFUL CHANGING AVATAR CAPTAIN JEAN-LUC PICARD, do you have anything for us?

[jean-luc]

Whoops! Ignore me! Posted a half-written post cause I'm dumb.

[jean-luc]

(The following is shamelessly stolen from wikipedia)

 

You are offered two envelopes, each with an amount of money. One envelope has double the amount of money that the other envelope has. There is no way to tell how much money each envelope has. You are allowed to pick one, and once you do, you're allowed to switch. I'm going to show you why you should always switch, and you have to tell me why I'm wrong.

 

Assume the envelope you have gotten has $10. If the other envelope is half, it will have $5. If the other envelope is double, it will have $20. So, on average you will get $5*(1/2) + $20*(1/2) = $12.50, which is more than what you started with. Therefore, you should always switch.

 

What is wrong with my argument?

[sushi]

Ok, first thing I did was Monte Carlo it. Not because it's so hard to calculate the probability, but because I do this pretty much every chance I get.

 

import random
x = 100000
y = 0
z = 0
while x > 0:
z = random.randrange(0,2)
if z == 1:
	y += 20
else:
	y += 5
x -= 1
print y

 

I got 1246730. Divide that by 100,000, and you get 12.46 -- very close to $12.50. Running it ten more times, I always got a number between 12.44 and 12.54.

 

If I were calculating the probability, I wouldn't write it as $5*(1/2) + $20*(1/2). I'd rather write it as (5 + 20) / 2. But the results are the same: 12.5.

 

I'm not seeing anything wrong with your argument.

 

I'll come back and look at this again though. See if I can find something I missed.

[sushi]

Wait a minute. Is it that you used the word "therefor" instead of "therefore"? Therefor means "for that object or purpose". It's usually used by lawyers, not logicians.

[jean-luc]

No, I had no idea there was a difference. My mistake :P

[sushi]

Well, in that case this would seem to be a variation on the Monty Hall problem. And in that one, it is a good idea to switch. Though in that one there are three options, not two, and you don't get to see what your option is -- you get to see what one of the other options is.

 

Wait, do I get to see the $10? Or are you just saying hypothetically there's $10 in the envelope that I picked? Actually, it shouldn't even make a difference. There's a 50% chance that I picked the right one, and a 50% chance that I picked the wrong one, no matter what my envelope contains.

[jean-luc]

You get the option to switch before you have any idea what amount of money is in the envelope.

[sushi]

But since I can't know how much is in the other envelope, it doesn't matter how much is in my own. All that matters is that I have no way of knowing, so there's no value in switching. Though it wouldn't hurt my chances to switch either.