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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)

#291

Post by jonasenordin »

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.

I think if you buy a first ticket, and somehow found out (but lotteries usually don't allow this) that it wasn't a winner, and only _then_ buying a second one, your reasoning would be correct.

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

#292

Post by A_No_Name_Mouse »

amscanne wrote: post #285
Cpoll wrote: post #283

Earlier quoted context omitted.

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…

I don't think this is correct. It matters whether the person removing the second ball can see the colors and choose accordingly. If you can, and you willingly remove a single blue ball, you have the Monty hall problem where you stick to your choice. It does not influence the chances, it is still 1/2. But the way I read the problem, you choose a ball at random, look at its color, it happens to be blue. Now this gives you information on the composition of the remaining balls. The chance is 1/3. To drive home the point that removing a ball "can influence" the odds of the first ball: what if you took out an extra ball that turns out to be blue? You now have two blue balls, leaving the chance the first ball was blue zero.

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

#293

Post by js2 »

> In Joseph Bertrand’s box paradox (1889), three boxes are presented -- one containing two gold coins, one containing two silver coins, and the final containing one of each. Assuming the participant draws one gold coin from a box, the problem then asks what the probability is that the other coin in that box is gold. Bertrand, who concluded that the probability was ⅔, was lauded for his ability to look beyond the obvious.

The initial distribution is:

    [gold, gold] [gold, silver] [silver, silver]
With six possibilities for drawing a coin:

    1. [----, gold] [gold, silver] [silver, silver]
    2. [gold, ----] [gold, silver] [silver, silver]
    3. [gold, gold] [----, silver] [silver, silver]
    4. [gold, gold] [gold, ------] [silver, silver]
    5. [gold, gold] [gold, silver] [------, silver]
    6. [gold, gold] [gold, silver] [silver, ------]
After drawing gold, you are left with:

    1. [----, gold] [gold, silver] [silver, silver]
    2. [gold, ----] [gold, silver] [silver, silver]
    3. [gold, gold] [----, silver] [silver, silver]
In 2/3 of the scenarios, you drew from box 1 and the remaining coin is gold. In 1/3 of the scenarios, you drew from box 2 and the remaining coin is silver.

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

#294

Post by fastball »

leephillips wrote: post #287
fastball wrote: post #274

Earlier quoted context omitted.

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 Ph…

Yeah I understand when we do it, I just don't agree with the why.

If I'm not gonna use a different prefix for accomplishments in a more generalized sense, I'm not going to lend extra respect / deference to people who some college I've never heard of decided were worthy of a PhD (or similar).

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

#295

Post by leephillips »

fastball wrote: post #294
leephillips wrote: post #287

Earlier quoted context omitted.

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 Ph…

Yeah I understand when we do it, I just don't agree with the why. If I'm not gonna use a different prefix for accomplishments in a more generalized sense, I'm not going to lend extra respect / deference to people who some college I've never heard of decided were worthy of a PhD (or similar).

Well, as my friend said after he got his PhD in philosophy, “Now they can send those welfare checks to Dr. .”

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

#296

Post by MarkMc »

To me the best explanation of the Monty Hall problem is to imagine there are 1000 doors. You pick a door and the host opens 998 other doors. Since you almost certainly did not choose the correct door, the host has almost certainly identify the correct door, so you should change your guess.

Then apply the same logic for 100 doors, then 10 doors, then 3 doors.

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

#297

Post by failwhaleshark »

failwhaleshark wrote: post #128
fastball wrote: post #66

Earlier quoted context omitted.

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.

Spies Like Us - Doctor, Doctor...

https://youtu.be/9UZWfMgjqAs

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

#298

Post by failwhaleshark »

leephillips wrote: post #179
failwhaleshark wrote: post #128

Earlier quoted context omitted.

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.

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.

I don't know about "losers," but maybe insecure- or envious-behaving people.

I was never told what my IQ tests were, but the educational system kept pulling me out of class to arrange triangles for years. Later, I was lazy and took the SAT without coaching, prep, or studying. Missed one on the math section, but let's not talk about the English section. ;@)

I don't even believe in IQ tests as a valid, quantitative, reductionist, relative-performance ranking for anything other than taking IQ tests. Intelligence is multidimensional, multi-domain, difficult to linearize to orthogonal properties, and inferred based on a particular performance, not quantified directly by opening-up someone's head.

Can't people just be people better in some areas? I can't draw for beans, my handwriting looks like I have advanced Parkinson's, and the neighborhood animals tip me to not sing in the shower.

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

#299

Post by dvfjsdhgfv »

dekhn wrote: post #279
glitchc wrote: post #236

Earlier quoted context omitted.

The host can never choose the door with the car, because then the game is over. Ergo the host has to choose the door with goat, every time.

this constraint was unclear to me in the original problem statement, which is why I thought she was wrong, too. It wasn't until somebody wrote in a letter saying they wrote a computer program that I understand what the rules were, and then it was obvious. I wish the problem was stated more clearly to say, the host has to choose the door with goat.

> I wish the problem was stated more clearly to say, the host has to choose the door with goat.

Yes, that one point would make many people instantly realize the probability changed. Nevertheless, you'd think mathematicians and statisticians sending her offensive letters should've known better.

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

#300

Post by jVinc »

dllthomas wrote: post #168
jVinc wrote: post #147

Earlier quoted context omitted.

> as it changes the answer. It doesn't. If the host randomly reveals a car, then you have 0% chance to win. If he doesn't you have 66% chance to win by switching.

I once thought that had to be the case. I wrote the simulation to demonstrate that I was correct. I learned that I wasn't. I encourage you to do likewise. I think I now have an understanding of why the right answer is the right answer, but I thought I had that before; I am more confident in the answer than my reasoning.

I owe you an apology, you're correct, I was wrong. I can't pinpoint where my reasoning failed me exactly, but my confidence certainly was misplaced, and that's from someone who did do the simulation originally to understand the outcomes, but not to understand the distinction between the host deliberately or randomly revealing the door. I'm sorry, but thank you for you persistence in correcting me. It was a fruitful learning experience to dig into this problem again.
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