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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)

#131

Post by marcosdumay »

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…

It's the presenter sharing knowledge with you, by opening a door that isn't the one you choose nor one that has the prize that changes the odds. And it doesn't help you if you stay with the same door because he never opens your door anyway, so it only adds knowledge about the other doors.

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

#132

Post by devilduck »

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.

There was plenty of actual sexism launched at her "wizard"

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

#133

Post by amluto »

TchoBeer wrote: post #64
dllthomas wrote: post #34

Earlier quoted context omitted.

Interestingly, if the host picks randomly (and if he reveals the car, you... start over, or you get the car, or you get nothing, or ... it doesn't matter because it happens not to have happened in the time we're considering) then you are faced with a 50/50 chance.

I don't understand how this could be. If you start over when the host picks the car, then isn't that the same as the host picking the goat every time, i.e. the same as the host knowing.

No, because the probability of a do-over depends on whether the contestant initially picked the door with a car.

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

#134

Post by jVinc »

TchoBeer wrote: post #87
jVinc wrote: post #61

Earlier quoted context omitted.

> vs "the treadmill moves backwards to keep plane airspeed at 0". You might be correct in thinking people misunderstand it as that, but that's physically impossible, so I don't think you can argue that people have some sort of alternate understanding under which they are actually correct. That's just one type of wrong reasoning people might apply to the problem. Add to that, in your hypothetical understanding of Mont…

It's great that you're so sure of yourself, just a shame that you're wrong. If the host picks randomly, your chances are in fact 50-50. Think of it this way: imagine every time the hosts picks the car the universe resets. Now imagine you see the host picking a goat. There's a 2/3rds chance in your universe you picked the car, and a 1/3rds chance you picked a goat, and so switching would seem like the bad option. This…

It's funny to me that there always seem to be an over representation of rude people among those who get this problem wrong. There is absolutely no need to attack my person.

As for the problem, you are just plain wrong. We are talking about are regular old TV-quiz, there is not "universe resetting button" to save your logic.

In the regular situation, the host always remove a goat. because otherwise the quiz show is kinda boring. But in the modified version we are considering where he just picks a door at random, then in 2 of the 6 possible outcomes for the door the host picks, he'll be removing the car. Now since the problem has the host showing the doors content, that should be the end of the game show. Who want's to see someone pondering if they should switch between a goat and another goat right? But that doesn't change the logic at all, because the conclusion of "you should always switch" isn't impacted in any way. 0% to 0% is just no change. And in the rest of the cases your'll go from 33% to 66%.

Now of cause what would happen in your odd example where the host has a universe resetting button is that you don't have any choice at all, because no matter what the host will reset the universe until they maximize ratings, which might have you get the car or might have you not get the car, but there's no choice to be taken and the outcome that has maximum rating will always happen with 100%. That's why most stats problems avoid introducing "then the host resets the universe" in their problem description, it kind of ruins the whole point of calculating proabilities.

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

#135

Post by ALittleLight »

saeranv wrote: post #79
GlenTheMachine wrote: post #38

Earlier quoted context omitted.

This particular one isn’t that hard to just do by hand. Which I did at the time, was surprised at the result, and stared at the column long enough to convince myself why she was right.

Using Bayes theorem? But if you know to use Bayes theorem, then you're already formulating the problem correctly, which is the problem all the critics are running into. Edit: Someone mentioned you could manually "simulate" it with a pen and paper, which I think is what you meant. If so, very good point.

I was unable to convince my father of this, so he and I just put together a little model with paper plates and coins and carried out the simulation manually until we had twenty or thirty trials and he became convinced by seeing it in action.

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

#136

Post by version_five »

One appealing thing to me about math is how egalitarian it is. It doesn't matter where ideas come from, they are probably right or wrong. It is (maybe unhealthily) rewarding to see critics acting like its another discipline where the senior or otherwise higher status person's opinion has more weight, only to make themselves look ridiculous. Contrast this with so many workplace things where senior people say dumb or incorrect stuff all the time but there is not the same objective way to call them out on it.

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

#137

Post by [deleted] »

failwhaleshark wrote: post #99

This reminds me of the time my entire family screamed and shouted that I was wrong that buying two different lottery tickets slightly more than doubles the total (infinitesimal) odds of winning over just one. 1 in a zillion vs slightly greater than 2 in a zillion because eliminating one choice reduces the pool by one for the next choice.

[deleted]

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

#138

Post by antonvs »

dunham wrote: post #84
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…

The thing that bothers me about this problem is that (as far as I recall) it's not asserted that the host always gives the player a chance to switch. If the host sometimes gives people a choice and sometimes doesn't, based on unknown criteria, then all bets are off.

In the probability puzzle, the chance to switch is part of the basis of the puzzle. It is always offered.

In the actual game show, the rules were more flexible. The OP article mentions this. For example, the host could "offer the contestant cash NOT to switch." That introduces a more psychological poker-like aspect, but that example still allows for switching and doesn't change the underlying probabilities.

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

#139

Post by lamontcg »

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…

Look at it from actual door, first guess door pairs -- which are the random uncorrelated events:

1,1 - switch loses (host may have shown door #2 or #3)

1,2 - switch wins (host showed door #3)

1,3 - switch wins (host showed door #2)

2,1 - switch wins (host showed door #3)

2,2 - switch loses (host may have shown door #1 or #3)

2,3 - switch wins (host showed door #1)

3,1 - switch wins (host showed door #2)

3,2 - switch wins (host showed door #1)

3,3 - switch loses (host may have shown door #1 or #2)

The choice of which door to show you is not a random event and is highly dependent upon the events which preceded it, because the host cannot show you the door it is actually behind, or the door that you picked.

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

#140

Post by paxys »

froh wrote: post #95

> Whereas only 8% of readers had previously believed her logic to be true, this number had risen to 56% by the end of 1992, writes vos Savant; among academics, 35% initial support rose to 71%. that 71% leaves 29% of _academics_ not getting the elementary math of the problem. I'm baffled this is _that_ hard?

"Academics" is a very loose definition. I imagine a very low percentage of PhDs out there have studied math seriously beyond a middle school level.
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