A brain teasing probability puzzle

Tuco_sl said:

Iannis you talking about

I'm surprised you're surprised it looks like that.... I always thought that molecular diagrams were somewhat accurate (If arbitrarily 2 dimensional) representations of matter.

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A different picture from that series, but yeah.

It still blows my mind. They are actually arranged in those physical shapes. I don't know what I expected exactly. Undulating amorphous blobs that project directional forces, creating paths of most and least resistance which promote the emergence of form maybe. But not exactly form itself. To me it's a more amazing thing that imaging the atom. Technically I suppose the atom is much more impressive but the atom is just a moment in time, these things are form.

And before we had any empirical evidence of it whatsoever, we intuited and refined that model. It's not conceivable to me that our model is the only possible accurate model. But there it is.

hodj_sl said:

Yeah the lottery is a tax on the poor and stupid.

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haha yeah, I feel the same about extended warranties too. Sure I may have a couple red ringed Xbox360s collecting dust...but overall I've saved a lot by not buying those things.

They're good on some things. Mostly flatscreen televisions. I've had two of those things burn out after 6 months and it's so much easier to pay the store 15 bucks to take it back than it would be to mail it to where-the-fuck-ever street warehouse in Asshole, USA to get it replaced.

yaw its still a 50/50 shot

How is anyone confused by this? Fucking morons.

Best way to explain this is: say there's 100 boxes and 1 has the prize. You choose a box and the host eliminates all but your box and 1 other.

Do you still think you have a 50/50 chance whether you switch or not?

It's the same principal except in this situation you have a 99% chance of being right by switching instead of 66%.

And apparently someone else barely beat me to it, probably because I had to type it in my phone

Dates?

That's where I stick my penis in a girl and then don't talk to her for a week, right?

Ambiturner_sl said:

Best way to explain this is: say there's 100 boxes and 1 has the prize. You choose a box and the host eliminates all but your box and 1 other.

Do you still think you have a 50/50 chance whether you switch or not?

It's the same principal except in this situation you have a 99% chance of being right by switching instead of 66%.

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This explaination cleared it up for me. Sure, it'spossiblethat you could have picked the correct box on the first try but, since there are 100 boxes, mostly improbable. But by now eliminating all but 1 of the remaining boxes, the probability of the prize being inthatbox is much, much higher.

But if out of the remaining 99 box the host only opened the one? Would you change your pick for the marginal statistical boost or trust your initial instinct?

Szlia_sl said:

But if out of the remaining 99 box the host only opened the one? Would you change your pick for the marginal statistical boost or trust your initial instinct?

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That was gone over earlier in the thread and it is called a multi-stage Monty Hall. You stay until the last choice, then switch. Switching is still the right answer statistically.

I can't believe people are still arguing this. The original question is, sadly, not the Monty Hall problem because the motivations of the game host are not spelled out. If he will always reveal the $1 box if it was not chosen and then he reveals the middle box then you should obviously switch, because you've chosen the $1 box. If he will choose a box at random to open not knowing what is in it, then there is a 50% probability that you have chosen the high box and it doesn't matter. Basically a high, mid, low box problem is dumb with 3 boxes.


Now, if the problem instead stated to be 2 lows and a high, then you have the Monty Hall problem and you should switch all the time.

Given the way the problem is laid out, the first choice is a false choice. The game ends up the same whether you beat the odds the first time and chose the winning box or not. In the end you have the choice of TWO boxes. The one you initially picked and the box the host didn't open. One is ALWAYS the winning box and one is ALWAYS a loser. The odds for the second choice are exactly same after the first choice no matter how many boxes you started with.... 50/50.

Kaines_sl said:

Given the way the problem is laid out, the first choice is a false choice. The game ends up the same whether you beat the odds the first time and chose the winning box or not. In the end you have the choice of TWO boxes. The one you initially picked and the box the host didn't open. One is ALWAYS the winning box and one is ALWAYS a loser. The odds for the second choice are exactly same after the first choice no matter how many boxes you started with.... 50/50.

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before anyone else starts arguing, may i ask your political affiliation and educational level?

Independent. Juris Doctor. Now, refute the statement that the game ends up the same every time no matter which box you initially picked. You have a 50/50 in the second choice. The first choice is meaningless whether you picked the winner or not.

Kaines_sl said:

Independent. Juris Doctor. Now, refute the statement that the game ends up the same every time no matter which box you initially picked. You have a 50/50 in the second choice. The first choice is meaningless whether you picked the winner or not.

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The act of taking away one of the $1 boxes reveals no new information - there will always be at least 1 $1 box to remove. The second choice is effectively the choice to take either your initial pick or the maximum of the other two boxes. Switching is always positive expected value.

QED You are a fucking moron.