^ Every now and then, it is true that I am the only one who sees the right solution to something. Other times it is someone else, but I keep an open mind about it.
The "actual solution" is as I've already stated multiple times, but unfortunately you are incapable of opening your mind enough to see it.
You were never very good at directions were you? It is very easy to see where this goes wrong, in that one gold coin was removed, which necessarily has a unique designation for the calculation to be plausible, but then the calculation considers the state where either designation could be picked which is impossible when only one coin of each designation exists picked and unpicked at any one rendition of the puzzle.
Don't understand it? Don't feel bad, apparently you're not alone. Strange things like this happen where masses of people are tricked. Hey, Trump was elected lol!
This is my exit post, no sense continuing, nothing more to say.
100 people are in a room, 98 are female and 2 are male. One of the males is missing his left nut. I pull aside one of the guys and squeeze his right nut, what are the odds that this guy has a left nut?
*bold added.It's not that we don't understand how they came to the 2/3 conclusion, rather it's that Bertrand's, and your, logic is wrong. It's that you, and Bertrand, don't understand how to apply statistics to this problem, in the context of how it is posed in the question.
Once the stipulation is made that the first coin is gold, there are only two boxes to consider, but also only two coin colors. Because it was worded that way, there is no 3 in the calculation.
Look at the video at 1:57 where it was stated "there are 3 possible outcomes". This is in error. The first coin could have been either G1 or G2, that does not matter because it was only established that a gold coin was chosen, not a specific gold coin. Next probability was stated as choosing a 2nd gold coin, but again not a specific gold coin, so the choices G1 and G2 in the video are the same outcome because they are both gold coins.
The only valid answer is 50% (1/2) because G1 and G2 cannot be distinguised as different choices based only on the parameter of choosing a gold coin. There is no way to differentiate G1 and G2. The variable of gold is equal for both, so G1=G2, or they are both G1 and there is no G2 if you prefer to state it that way. G1/G2 and G2/G1 are both the same choice, cannot be enumerated separately.
Care to elaborate? It's not necessary to disprove something that is already logically impossible and in error. An infinite # of reasons why something is wrong is not needed, only ONE reason.
It is simple fact that the only variable was gold vs silver, and thus G1 must equal G2 until another variable is introduced, something like heads up or down, different denomination, etc.
*bold added.
Two boxes, each with two balls. Equals 4 balls total. Following?
You've already chosen one ball. 4 - 1 = 3 options for the remaining ball. Still following? As you stated there are only two boxes to consider, because the other boxes can't have the gold you picked first.
Shirley you can see where the 3 comes from now.
As you said there are two boxes, with 3 gold in them and 1 silver. G1, G2, G3, & 1S. Four options, you chose one of the golds already so you have 3 possible choices next.
The "only variable was gold vs silver" is true. And this variable is a ratio of 2 golds to 1 silver, since they all have an equal chance... 2/3 it's the box with 2 gold.
The simple fact you're missing is that we're not choosing between the boxes (2 options), the question is to choose the next ball (3 options) which then tells us which box it's from.
It's cool to be an independent thinker. And everyone has the right to think and say whatever they want. But that doesn't mean they're correct. And it doesn't mean it's correct to dig your heels in. Sometimes in subjective situations standing up for your choice is worth something, and sometimes standing up for you choice is stupid, stubborn, and ignorant.
Like most trick math questions, it's just boils down to a game of words and punctuation, and playing hide the ball by using a badly worded question that freely intermixes statistical terminology with colloquialisms.
If you go by the colloquially worded last statement, the answer is 50%, because it leaves the question as a coin toss. Its only 66% because it's a trick question by not telling you that the answer has to follow conventions of academic statistics.
This question basically illuminates the crux of all real life debate arguments. Partisans on either side are playing word games and leave their own internal premises unspoken and are ultimately talking past each other by operating under different rules in order to score points with their tribe.
Because the answer Bertrand provides is wrong. Not as in, we're dumb and this is the internet -wrong, but rather as in "its 2018 and we understand quantum states" -wrong.
Like most trick math questions, it's just boils down to a game of words and punctuation, and playing hide the ball by using a badly worded question that freely intermixes statistical terminology with colloquialisms.
If you go by the colloquially worded last statement, the answer is 50%, because it leaves the question as a coin toss. Its only 66% because it's a trick question by not telling you that the answer has to follow conventions of academic statistics.
This question basically illuminates the crux of all real life debate arguments. Partisans on either side are playing word games and leave their own internal premises unspoken and are ultimately talking past each other by operating under different rules in order to score points with their tribe.
I'm impressed with the few people who changed their mind about the answer to the riddle. I'm less impressed with a lot of the other stuff.
If there was to be an intelligent discussion about probability then post # 2 would have asked to restate the problem using statistical notation to avoid all of the problems that come up from using the wrong language. That wouldn't be any fun for us high IQers who enjoy watching the mental peasants squabble over what's right and wrong though.
That probably didn't happen because there isn't any confusion outside of those desperate to prove their wrong answer / interpretation is not wrong. This isn't the bible here guys.
That the OP was left open for interpretation at all, and that some information had to be disregarded as trolling, kinda proves that there was confusion by those desperate to prove their right answer too.
Badly coded. There is no real life equivalent where something that can hsppen (SG1) does not happen. As already pointed out.And yet real life trials show he was right, funny how that works
The only language barrier is understanding what a random choice means and what a probability is, which doesn't require an academic background in mathematics (though it does help). As long as you know what they mean, the rest of the problem is clear to solve, the solution is just very counter-intuitive. If you don't understand what those two words mean, you'll have real trouble solving the problem correctly.
It is too hot to think about these things. I am clocked down and mostly powered down. I just want to sit still in the air of the ventilator while digesting my food. And listening to good music.
This whole stunt is just about what probability exactly means.
It's counter-intuitive because it requires a very specific interpretation of the question, including ignoring the way the question is nested.
The interpretation required to solve it is: "Even though the question is posed as if it's a coin toss scenario, pretend like the question actually asks for the probability of the entire scenario. Also ignore any extraneous details like the imposition of "you" and all it's baggage, and assume the beginning of this scenario is T:0 at the beginning of a universe that was willed into existence with no priors."
I would say poorly worded questions result in problems that don't get solved well, and this correlates to real life as well--poorly constructed corporate projects gives way to predictably poor results as well. Seems like this is a good question to pose to management trainees, with the correct answer being: "Ask better questions."
Badly coded. There is no real life equivalent where something that can hsppen (SG1) does not happen. As already pointed out.
The only states which exist in the system described are G1S + G2G3 and G1S + G3G2. If you code that, you will see the 50% answer.
I wrote this clearly earlier but was ignored. I also wrote what the OP must state to result in 66% but was ignored.
I chose to use the phrase "quantum states" because the likelyhood of events between one state and the other is not affected by the previous, such as physical location of photons during a measurement. Specifically, once a gold ball is drawn, a portion of possible states can no longer exist, but Bertrand takes a step back and includes them in his calculations. He writes a problem, and then proceeds to give the answer to a different problem.
This doesn't even make sense. First you state the problem was left open to interpretation, and then agree there is a right answer. You can't have a right answer with ambiguous interpretation (unless the answers are equally the same to all interpretations, which isn't the case here).
Vanilla Ice will cool you down
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