A brain teasing probability puzzle

Tanoomba_sl said:

Dude, the most hilarious part of all your claims is that simulating the problem (either using the provided simulator or doing it with a friend and 3 playing cards) somehow produces incorrect result because it "works from the wrong premise that the first choice matters". What the hell does this mean?You're simulating the problem exactly as it's worded. You getconclusiveresults. If you think the results are "wrong" somehow then, clearly,you'rethe one working from the wrong premise.

If you pick the door with the car and change, you lose. If you pick the door with a goat and change, you win. Those are the two possible outcomes if you choose to change. This is the binary choice. But it is NOT a 50/50 choice. There is a 1/3 chance that you will pick the door and change. So, a 1/3 chance that changing will lead to a loss. There is a 2/3 chance that you will pick a goat and change. So, a 2/3 chance that changing will lead to a win. This is how it works.

Yes, it's impossible to win after the first round. However, you still either chose the door with the car (less likely) or the door with a goat (more likely) first. Changing your choice literally reverses those odds. If you picked a goat (which was more likely), you get to switch to a car. If you picked the car (less likely), you switch to a goat. I don't know how this can be made any simpler.

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I'm sure he's just trolling at this point. He probably argued this in good faith originally. But then a few pages in, he realized that he fucked up and was already in too deep to back-peddle, so he'd rather double-down on ignorance to save face than admit being a dumbass.

Soriak_sl said:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1) Linda is a bank teller.
2) Linda is a bank teller and is active in the feminist movement.

Statisticians get this one wrong all the time.

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2) is a subset of 1), so, no matter what, 1) should be more likely... but that sounds like the answer a statistician would give...

Szlia_sl said:

2) is a subset of 1), so, no matter what, 1) should be more likely... but that sounds like the answer a statistician would give...

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It's also the right answer. I don't get why any statistician would get that wrong. Seems to me people more interested in their intuition and less interested in the math would get that wrong.

Szlia_sl said:

2) is a subset of 1), so, no matter what, 1) should be more likely... but that sounds like the answer a statistician would give...

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It was so obvious to me that the answer is 1), but knowing it was a trick question, I had to google it to see what the 'gotcha' was, since I had to be wrong to answer it so fast.... Only to find that the answer is 1). I really don't know anyone could possibly answer 2). Something more general is always more probable than something specific. How is that not extreme common sense?

As to Araysar, I don't think his problem is with the math per se. His issue is he doesn't understand that the first choice matters. He see's that under all cases, the host throws away an option, so he thinks you can safely just ignore his action. Ignoring him since 100% of the time he picks a goat, your really only left with 2 choices: Your door has a car and the other door has a goat, or your door has a goat and the other door has a car. Hence 50/50.

Zuuljin_sl said:

It was so obvious to me that the answer is 1), but knowing it was a trick question, I had to google it to see what the 'gotcha' was, since I had to be wrong to answer it so fast.... Only to find that the answer is 1). I really don't know anyone could possibly answer 2). Something more general is always more probable than something specific. How is that not extreme common sense?

As to Araysar, I don't think his problem is with the math per se. His issue is he doesn't understand that the first choice matters. He see's that under all cases, the host throws away an option, so he thinks you can safely just ignore his action. Ignoring him since 100% of the time he picks a goat, your really only left with 2 choices: Your door has a car and the other door has a goat, or your door has a goat and the other door has a car. Hence 50/50.

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Nah, he gets it. He may not have gotten it in the beginning, but even a retarded monkey would have gotten it by now. He gets it, and he knows hes wrong. But hey, sticking with ignorance is less wrong than reversing yourself and admitting that you were wrong in the first place.

Yeah, he gets it, but is too proud to admit it. You have to be Merlin level stupid to not understand it by now. A once great man said:

Araysar_sl said:

If anything, I think the ability to admit that you're wrong is a fairly impressive character trait.

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Anyway, it puts him in the same team as Aladain in the poll results:Bootsand50/50.

Erronius_sl said:

Probably for the same reason that you had to go Google it - it sounds like a trick question and I'm guessing people start questioning their first answer.

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In the original experiment by Tversky and Kahneman, 90% of respondents picked answer 2. If you make a quick decision on it, then the "feminist" part seems more representative of Linda, which is why people go with it. There are variations that report fewer people picking #2, but it's still a majority (goes down to like 60% if you rephrase it somewhat).

The reason everyone here is going to get it right is because it's in a thread on trick questions. But a whole lot of people will answer these questions without giving it much thought, simply picking the first answer that feels right. You do not get 90% picking a wrong answer without some underlying cause...

I had mentioned the cognitive reflection test. Here are the 3 questions for that one. Go through it quickly and note the first answer that jumps to mind.

A baseball and a bat cost $1.10. The bat costs $1 more than the baseball. How much does the baseball cost?

If 100 machines take 100 minutes to produce 100 widgets, how long do 500 machines take to produce 500 widgets?

A patch of lillypads doubles in size every day. After 48 days, they cover the entire lake. How long does it take until they cover half the lake?[*]

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[*]This is actually a really unrealistic example. If you start with a 1cm^2 patch of lillypads, they will cover an area half the size of Germany in 48 days.

wormie_sl said:

2 is not a subset of 1 because 2 is two seperate sets. If 2 was a subset of 1, that would mean a set containing all tellers is the same size(or bigger) than a set containing all tellers AND all feminists, which is obviously not the case. So, while your answer is correct, the assumption you used to derive that answer is not.

1 is correct because the set of all tellers is bigger than the intersection of a set containing all tellers and a set containing all feminists.

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What? A set containing all tellers and all feminists would be the inclusive OR set, not AND. The question states Linda is tellerandfeminist, not tellerorfeminist. AandB is the intersection of 2 sets. Since an intersecting set is a subset, 2 is in fact a subset of 1. Or did I miss something?

Maybe that's the trick of the question. People assume 'AND' means addition. Somethingandsomething else must be larger than just something. When in this case, AND is actually less than the original set.

Zuuljin_sl said:

Maybe that's the trick of the question. People assume 'AND' means addition. Somethingandsomething else must be larger than just something. When in this case, AND is actually less than the original set.

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I'm pretty sure the trick of the question is that people think 1 and 2 are mutually exclusive. They interpret the choices as:

1. She's a teller, AND NOT a feminist.
2. She's a teller AND a feminist.

Since the extra information suggests that she's a feminist, they automatically pick 2. They don't consider that the probability that "she's a teller" already includes the probability that she's a teller and a feminist.

Araysar_sl said:

Voyce, I appreciate the effort you put into it. I will take a look at it some time later today. I've been doing a lot of other accurate math today, so I'm kinda wiped out for now.

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Ok, since you still seem to be open to reason, let me also give it a shot to explain.

Round 1: In the first round, your pick has a 1 in 3 chance to contain the car: p(your pick) = 33%
Round 2: The host opens one of the two unselected doors, revealing a goat. So now there are 2 doors still unopened, with a 100% chance of one of them containing the car. It's either behind your pick, or behind the other door. We know from step one that p(your pick) = 33%, so now we can derive that p(the other door) = 100%-p(your pick) = 100%-33% = 66%
So the strategy of always switching results in having a 66% win chance.

If this doesn't break the mental barrier down that blocks you from 'seeing it', try envisioning it with the 1000 doors variation.
Round 1: There's a 1000 doors, with 1 car and 999 goats behind. You pick a door. It has a 1 in 1000 chance (0.1%) of having the car.
Round 2: Now the host opens all other doors except 1. So he reveals 998 goats and leaves one door unopened. Then he asks you if you want to switch. You know the car is either behind your first pick, or behind the one door he left unopened.
Well, since your initial pick only has a 0.1% of being the correct door, the other door has a 100%-0.1% = 99.9% chance of containing the car. Again, to switch is the right strategy.

Soriak_sl said:

In the original experiment by Tversky and Kahneman, 90% of respondents picked answer 2. If you make a quick decision on it, then the "feminist" part seems more representative of Linda, which is why people go with it. There are variations that report fewer people picking #2, but it's still a majority (goes down to like 60% if you rephrase it somewhat).

The reason everyone here is going to get it right is because it's in a thread on trick questions. But a whole lot of people will answer these questions without giving it much thought, simply picking the first answer that feels right. You do not get 90% picking a wrong answer without some underlying cause...

I had mentioned the cognitive reflection test. Here are the 3 questions for that one. Go through it quickly and note the first answer that jumps to mind.


[*]This is actually a really unrealistic example. If you start with a 1cm^2 patch of lillypads, they will cover an area half the size of Germany in 48 days.

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Araysar_sl said:

I picked 1 right away. Clearly, the more specific the conditions, the less likely they are.

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And yet, after 6 pages, you still can't admit you are incorrect about the Monty Hall problem.

Dear baby jesus, please rickshaw this whole mess or rename it the "Araysar trolls the shit out of everyone" thread.

I'd hate to see what would happen if we were debating technically complex scenarios instead of one of the oldest (and completely settled) problems around