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The Time Everyone “Corrected” the World’s Smartest Woman (2015)

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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#121

Post by 6gvONxR4sf7o »

lachstar-x wrote: post #102
6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

Can you help me understand - in my view the choice to switch doors or keep the same door is irrelevant, because even if you keep the same door you're making a choice that is now 2/3 of the right answer. If you switch or keep, you're still choosing from two doors that contain a car and a goat. The other door is no longer relevant and doesn't affect the new state at all. It's your perspective (narrowing the choice down…

I wrote out a hopefully helpful intution down below [0]. Here's a terse part of it:

> Or just imagine monty hall with infinite doors. I'm thinking of a number between 1 and infinity (secretly, it's 19083412039102388171230123). You pick a number, and then I'll narrow down your choice to two options. Do you think you just happened to pick my number, or do you switch?

You're right that it's absolutely the narrowing down of the choice that's the key. If you happen to have not picked the prize door on your first try (more likely than not), the narrowing down will be your door and the prize door.

[0] https://news.ycombinator.com/item?id=27092614

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#122

Post by zeroimpl »

lachstar-x wrote: post #102
6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

Can you help me understand - in my view the choice to switch doors or keep the same door is irrelevant, because even if you keep the same door you're making a choice that is now 2/3 of the right answer. If you switch or keep, you're still choosing from two doors that contain a car and a goat. The other door is no longer relevant and doesn't affect the new state at all. It's your perspective (narrowing the choice down…

The other door is not irrelevant.

When you first picked a door, there was a 33% chance it was right, and a 67% chance one of the other two doors was right.

Once the other door got opened, it is still a 67% chance that the other two doors is right, but you now know which one of those two it would be - the one which wasn’t opened.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#124

Post by jsjohnst »

pmiller2 wrote: post #22
saeranv wrote: post #9

I guess Monte Carlo simulations weren't well-known or easily accessible back then? It would have been the perfect way to shut up her critics.

You could do it in Excel in probably 20 minutes.

You could do it with a pen and paper in less than 5.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#125

Post by FabHK »

hn_throwaway_99 wrote: post #116
6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

In this case, though, I don't believe it's just calculation vs. intuition. The reason the 100 or million door problem helped me understand was because it clarified an implicit rule of the game: that the door the host chooses to open is not random . If it were random, it would make for a very boring game ("Uhh, there's the prize, you win, I guess that's game over.") Once I understood that the host would only ever open…

Indeed, that is a crucial bit of information that is not made explicit in the original framing of the problem.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#126

Post by 2muchcoffeeman »

6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

* Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness.*

It puzzles me that so many smart people got it wrong. It’s so easy to check your working.

When I first heard of this problem, I got it wrong too. Then I was told the answer, and to prove it to myself, it’s trivial to list the scenarios and simulate on paper. It’s still uncomfortable to think about sometimes, but I know how to show it’s true.

But all these people never thought to just do the working? Crazy!

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#127

Post by cableshaft »

Cpoll wrote: post #44

Another statistically unintuitive problem (which I've witnessed a lecture hall enter a state of uproar over): There are 2 red and 2 blue balls in a box. One ball is removed at random, what are the odds that the ball is blue? Now we repeat the problem, but before examining the ball, we remove a second ball. We observe that the second ball is blue. In this case, what are the odds that the first ball is blue?

Yeah, 1/3. Once I labeled them as R1 R2 B1 B2 and just listed all possibilities, it became clear where my error was.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#128

Post by failwhaleshark »

fastball wrote: post #66
calibas wrote: post #14

"You made a mistake, but look at the positive side. If all those Ph.D.’s were wrong, the country would be in some very serious trouble."

This is why I no longer call people Dr.

Lol. I worked at a biomedical informatics shop with IITians and other folks who were MD + PhD CS. No one referred to anyone as doctor and no one there took a MENSA test. I think it's safe to say the only "doctors" are clinical MDs, podunk colleges to seem elitist, and Spies Like Us during the surgery scene.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#129

Post by tanbog4 »

lachstar-x wrote: post #105
javajosh wrote: post #23

So this is at least in part about the "Monty Hall Problem" and why it's solution not intuitive. The article missed an important angle: when the host opens a door, he's giving you more information , which explains why it's better to switch. If you're the host, you need to know which door the car is behind to do your job 2/3 of the time, to avoid revealing it. It's this quality of unexpected information exchange that I…

Isn't he also removing relevant information as well? The third door is no longer part of the game so the information he gives you ceases to be relevant.

I don't think you can "remove" information from A probability problem in this way. And even if you could there's no reason to assume it would zero-sum with the later information gain.

Happy to be wrong though, been a long time since i dabbled in probably.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#130

Post by magnio »

nextlevelwizard wrote: post #107
macintux wrote: post #25

Earlier quoted context omitted.

Being wrong isn’t a crime. Harshly lambasting a woman for, largely, being a woman and disagreeing with you is the problem.

Jumping to sexist assumptions is also a problem.

So is not reading the article:

> Maybe women look at math problems differently than men.

> “I still think you’re wrong,” wrote one man, nearly a year later. “There is such a thing as female logic.”

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