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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)

#281

Post by dekhn »

ncallaway wrote: post #249
FabHK wrote: post #195

Earlier quoted context omitted.

That is literally not explicit (where by "literally" I mean literally, not figuratively, and by "explicit", I mean explicit, not implicit). It is sort of hinted at, but it is not explicitly said that the host will mechanically reveal a door that has a goat. It is quite conceivable that the host picks a door randomly, or in fact that he picks the door with the car with a certain probability (saving the show quite some…

> It is literally explicit in the 1990 rendition. > You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat Remove the parenthetical example "say #3", and the parenthetical "who knows what's behind the doors" and that sentence reads: "...and the host opens another door which has a goat". The "has a goat" is not a hypothetical example. It's a (both literal…

nope, it's ambiguous as stated, if you're a literalist.

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

#282

Post by TchoBeer »

stale2002 wrote: post #176
TchoBeer wrote: post #87

Earlier quoted context omitted.

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…

> imagine every time the hosts picks the car the universe resets Do you believe that we live in a universe that is reseting, every time Mr Monty hall opens a car? As in literally Mr Monty Hall. From the game show. In real life. Because the purpose of the question is to mimic the show.

You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car, and the result is the same.

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

#283

Post by Cpoll »

amscanne wrote: post #252
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?

Love it. The answer is 1/2. The first event occurs with a population of 2,2 and the second event has no causal effect. The trap is that the observation doesn’t change the sample population of the first event, exactly like the Monty Hall case: opening doors itself does not change the probability to 1/2 as people think it does (it remains 1/3) — it’s the switch that changes the odds. Similar question with a similar tra…

Take a look at the other replies. I like paxys' for the simplicity.

The second ball being selected doesn't change the first event, but it does change our understanding of it.

An extreme version: There's a bowl with 3 red and 1 blue balls. We remove two balls again, and the second one is blue. What are the odds that the first one is blue?

Your two kids problem is actually pretty complex, in the form you phrased it. Wiki has a decent explanation (I contend that your question is equivalent to the second question in the wiki article): https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

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

#284

Post by jonasenordin »

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?

This is turns out to be rather straightforward once you realize that this is perfectly symmetric: it's just a matter of in which order you are revealing the colors. So this problem is exactly the same as looking at the first (second) ball, seeing that it's blue, then drawing a (revealing the already drawn) second ball. So there are two reds and one blue 'left'. So 1/3. (I am 95% sure...)

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

#285

Post by amscanne »

Cpoll wrote: post #283
amscanne wrote: post #252

Earlier quoted context omitted.

Love it. The answer is 1/2. The first event occurs with a population of 2,2 and the second event has no causal effect. The trap is that the observation doesn’t change the sample population of the first event, exactly like the Monty Hall case: opening doors itself does not change the probability to 1/2 as people think it does (it remains 1/3) — it’s the switch that changes the odds. Similar question with a similar tra…

Take a look at the other replies. I like paxys' for the simplicity. The second ball being selected doesn't change the first event, but it does change our understanding of it. An extreme version: There's a bowl with 3 red and 1 blue balls. We remove two balls again, and the second one is blue. What are the odds that the first one is blue? Your two kids problem is actually pretty complex, in the form you phrased it. Wi…

I’m aware that it’s complicated. I intentionally phrased it in a way that makes it clear that the family moving in is not somehow selected from the set of families with at least one boy, but rather the observation is unrelated.

This is the distinction. I believe that the 1/3 analysis may also be incorrect for the way you phrased your question. If you had said: “we select a second ball, and only observe the first ball if the second is blue — what are the chances of it being blue?”, then the second observation controls the population. Otherwise it’s semantics over exactly what probability we are trying to define?

I think the issue with these questions is that we are asking about “probabilities” which only make sense with repeated iterations. So you always have ambiguity in the construction of the question and interpretation when asking about things that are a “one time” event like both these examples.

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

#286

Post by [deleted] »

fastball wrote: post #274
leephillips wrote: post #179

Earlier quoted context omitted.

Only losers take Mensa tests and talk about their IQs. But plenty of PhDs use the Dr title in the right context. It's just the height of jerkdom to insist on people addressing you with it.

What's the right context? Why are PhDs (and MDs) the only people that deserve a special prefix in our society? I know loads of people that have worked harder and smarter than people with PhDs, but they don't get a prefix.

[deleted]

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

#287

Post by leephillips »

fastball wrote: post #274
leephillips wrote: post #179

Earlier quoted context omitted.

Only losers take Mensa tests and talk about their IQs. But plenty of PhDs use the Dr title in the right context. It's just the height of jerkdom to insist on people addressing you with it.

What's the right context? Why are PhDs (and MDs) the only people that deserve a special prefix in our society? I know loads of people that have worked harder and smarter than people with PhDs, but they don't get a prefix.

So do I, but titles don’t mean that you are more worthy, they are just a convention that indicates a particular thing. For example, the titles Mr., Ms., Prof., and so on. Different countries and cultures use titles differently; in some societies, such as in the US, we use the title “Dr.” for someone who has received one of several (earned, not honorary) degrees from an accredited institution. These are the MD, the PhD, and some other degrees that have a D in them, such as the EdD (Biden) and the DrPH (doc. public health)¹. This is so even though these degrees involve little more than vocational programs with two years of coursework.

The right context are things like business cards, listing people’s names on the program of a conference, or any place where you want to indicate someone as a degree holder, to lend a little formality, indicate respect, or try to impress the innocent. It is no more incumbent on you to use the title as it is to use someone’s preferred pronouns. It’s up to you. And to make an issue of it is pitiful and boorish.¹

[1] https://www.thelily.com/a-white-city-official-refused-to-add...

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

#288

Post by ziml77 »

ronyeh wrote: post #115
lachstar-x wrote: post #102

Earlier quoted context omitted.

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…

Think from the perspective of your first choice. You had a 66.66% chance of choosing the wrong door. So now I just eliminate one of the doors you didn't choose. There are two left, including the one you chose first, which only had a 33.33% chance of being correct. Nothing else has changed about the problem. What if we started with a thousand doors? You chose 1, with a 999/1000 chance of being wrong. Of the remaining…

I like expanding it out to 1000 doors. Even though the logic is the same between 3 and 1000 doors, the chances are more intuitive with more doors.

I think the part that really throws the brain off with the 3 door version is that the host opening a door seems like another random event but it's actually dependent on the state of the game at that point. Our natural intuition of the chances is for a version of the game where you pick a door, then the host randomly picks (and does not open as you also haven't) a different door, and then you have to choose if you want to switch to the door that neither of you picked.

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

#289

Post by bordercases »

TacticalCoder wrote: post #117
lachstar-x wrote: post #102

Earlier quoted context omitted.

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 no longer relevant and doesn't affect the new state at all. There is no new state, that's the thing. By picking one door you split these in two groups: one group with 1/3 to win, the other with 2/3 to win. When the host reveals the door with a goat behind it from the group that is 2/3 to win, it doesn't change the fact that that group had 2/3 to win to begin with. I mean: that's how I see it.

It changes what you know. States are measured in the mind.

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

#290

Post by bordercases »

denton-scratch wrote: post #277
tomerv wrote: post #237

Earlier quoted context omitted.

At first I agreed with you, but then I thought about the variation with 100 doors (this is what originally helped me grasp the correct answer): you choose a door out of 100 (with very slim chance of choosing the correct one), the host opens 98 of the remaining 99 doors and there are goats behind all of them. Now it's obvious that the car is in the remaining door. If the host is opening random doors, then: * If you ch…

"Now it's obvious that the car is in the remaining door." No. It could be behind the one you chose, surely. I understand the explanations, or at least some of them; but I still don't get it. I thought I was intelligent and numerate, and this is making me sad. I don't see why, after Monty reveals a goat and invites you to switch, you can't re-assess the probabilities from scratch. There are two closed doors, car behin…

But you are presented with a new option with 50:50 odds and should take it. Since the original odds were worse.
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