A fun little probability puzzle for you.

What is the basis for reason? And mathematics?

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Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Fri Aug 12, 2022 4:32 am Why was the probability 50/50 before you pull out a $100 bill, but somehow it becomes 2/3 after you pull out a $100?
I've already answered that, multiple times now. If you want to understand how pulling out a $100 can give you probabilistic information about what box you likely have in front of you, then consider the example of 2 bags of blue and red balls.

If you have 2 bags in front of you, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and you choose a bag blindly, and you reach into it blindly and pull out a ball, and that ball is blue, you're going to rationally think that you probably picked that ball out of the bag that's full of blue balls, and it's much less likely that you picked that ball out of the bag that's mostly red balls.

It's only the same logic. When you pull out the $100, you're more likely to have pulled it out of the box that's full of 100s.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Fri Aug 12, 2022 9:15 am
Age wrote: Fri Aug 12, 2022 4:32 am Why was the probability 50/50 before you pull out a $100 bill, but somehow it becomes 2/3 after you pull out a $100?
I've already answered that, multiple times now. If you want to understand how pulling out a $100 can give you probabilistic information about what box you likely have in front of you, then consider the example of 2 bags of blue and red balls.

If you have 2 bags in front of you, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and you choose a bag blindly, and you reach into it blindly and pull out a ball, and that ball is blue, you're going to rationally think
1. Do not ever tell me what I would or would not 'rationally think'. The 'thoughts' with this head are not necessarily the same 'thoughts' within that head, and one set of so-called 'rational thoughts' inside of one head can be the complete opposite of so-called 'rational thoughts' within another head. So, what is 'rationally thought', by 'you' is not necessarily the same as, by 'me'. Do you understand this?

2. What 'you', human beings, so-call 'rationally think' does not necessarily relate to what is actually and irrefutably True, Right, nor Correct, either. Do you understand this?
Flannel Jesus wrote: Fri Aug 12, 2022 9:15 am that you probably picked that ball out of the bag that's full of blue balls, and it's much less likely that you picked that ball out of the bag that's mostly red balls.
But what you think is probably true does not necessarily mean that it is actually true. And, this again, is another reason why I do not like to assume absolutely anything at all.
Flannel Jesus wrote: Fri Aug 12, 2022 9:15 am It's only the same logic. When you pull out the $100, you're more likely to have pulled it out of the box that's full of 100s.
But this is not actual 'logic'. This is just what you 'think' is 'probably' true.

Let us not forget that your first so-called 'intuitive' thought is not necessarily the true nor right one.

Now, what we have here is that the reason that the probability that there is $100 bill remaining in that one box is 2/3 is because this one so-call 'rationally thinks' that it 'probably' picked the $100 bill out of the box with two $100 bills in it, and you may well have.


But to show the absurdity of this. If one tosses a coin one time or one million times and it comes up 'heads', then this one would so-call 'rationally think' that next time I toss this coin that it would 'probably' come up tails. But the fact is you could toss a coin a billion times and if each one of those tosses it came up 'heads', then the next time the coin is tossed the probability, or the chance, that it comes up heads OR tails still remains 50/50, and it remains the same no matter what you 'rationally' or 'intuitively' 'think'. All things being equal there are only two things to choose from. Therefore, the odds, or probability, always remain 50/50.

But, to get back to your, 'fun little probability puzzle, for you', to begin with there were ONLY two boxes to choose from. So, from the start there was only a 50/50 chance, or probability, that the box you picked was 'full' of $100 bills. Once you had your one box and had picked one $100 bill out of it the chance, or probability, that the bill remaining was a $100 bill or a $1 bill was also 50/50. This is because there could only be either a $100 bill or a $1 bill in it. It was a box with only one bill in it now. The chance, or probability, that it comes up to be a $100 bill or a $1 bill is 50/50. But besides these, logical, facts, which ended up going against my first 'intuitive thought' or 'intuitive guess' of 66%, the fact is there were not more than two notes in each of the two boxes, and because there was always only two choices to be made, along the way in your little probability puzzle here, the answer is and remains 50/50, correct? No matter what you 'rationally think' or 'intuitively guess'.

If however, there were more boxes to begin with and all but one box had two $100 bills in it, then that would change the probability, or if there were still only two boxes but one box had fifty $100 bills in it and one box with forty nine $1 bills and one $100 bill in it, for example, then, that you are more likely to pull a $100 bill out of the box that is 'full' of $100 bills in it is obviously more likely. So, IF you had the box with fifty $100 bills in it, then the probability, or the chance, that you pull out one $100 bill is so 'more likely' that it even reaches the 100% mark, BUT if you actually have the box "full" of $100 bills in it is still yet to be seen, and realized.

The probability that you picked either box was 50%.

The probability that you picked one $100 bill out of the box with two $100 bills in it was 100%

The probability that you picked one $100 bill of the box with one $100 bill in it and one $1 bill in it was 50%

To me, the probability that the remaining bill is a $100 bill or a $1 bill became, and still remains, 50%

But this view, obviously, could still be wrong.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Fri Aug 12, 2022 11:04 am
So in the blue balls example, when you pick the blue ball out of the bag, you don't think you're more likely to have selected it out of the bag full of blue balls? Do you think it's 50/50, after seeing the first ball you selected being blue, that the bag you have in front of you is the one full of blue balls? What do you think?
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Fri Aug 12, 2022 2:23 pm
Age wrote: Fri Aug 12, 2022 11:04 am
So in the blue balls example, when you pick the blue ball out of the bag, you don't think you're more likely to have selected it out of the bag full of blue balls? Do you think it's 50/50, after seeing the first ball you selected being blue, that the bag you have in front of you is the one full of blue balls? What do you think?
Did you read my reply?

The answer to each of your three questions is in there.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Sat Aug 13, 2022 12:25 am Did you read my reply?

The answer to each of your three questions is in there.
If you really think it's still 50/50, then... your intuitions about probabilities are so out of whack that we're basically just speaking entirely different languages here.

If I had one bag with all the grains of sand on a beach in it, and they're all perfect pearlescent spheres, and I had another bag with the grains of sand from another beach, and 1 of them was a perfect pearlescent sphere and the rest of them were grey, and you chose a bag at random, and picked out a single grain of sand at random without looking, and you looked at it and saw that that grain of sand was a perfect pearlescent sphere, you're really telling me that you're still going to say it's 50/50 which bag of sand you chose?
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

You know, you can test it yourself. All you need is 11 pennies and 9 dimes. Split them into 2 bags, 1 with 10 pennies and 1 with the rest.

Choose a bag at random, then pick out a coin at random. If it's a penny, record whether you picked the bag full of pennies or whether you picked the one penny out of the bag with 9 dimes. Do that experiment over and over again and find, out of all the times you pull a penny out, what percent of those times you pulled it from the bag full of pennies.

All the theory talk is pointless when a real experiment is both possible and easy to perform.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Or, think about it like this: when you know one property of something, it can tell you probabilistically about another property of something.

Let's say I have a classroom of 100 kids, and 2 of those kids are black, and both of the black kids have black hair, but only 1 of the other kids has black hair. So 3% have black hair, but all of the black kids have black hair.

Now, you're the principal, and there's a kid from my classroom, selected at random waiting outside your office. You know nothing at thi point about who that kid is, other than that he's 1 of the 100 kids. If I ask you, "What's the probability that the kid is one of the black kids?", what's your answer?

And now, I say, "The kid, who was selected at random, happenss to be one of the one with black hair. What' the probability now that the kid is one of the black kids?"

Does the probability change?

If it does, if you think that information changes the probability, then I'm only using the sasme thought process as that in my 50balls per bag example, or my 2 bills per box example. I'm simply usisng one property of an object to tell me probabilistic information about another property of that object.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 5:14 am
Age wrote: Sat Aug 13, 2022 12:25 am Did you read my reply?

The answer to each of your three questions is in there.
If you really think it's still 50/50, then... your intuitions about probabilities are so out of whack that we're basically just speaking entirely different languages here.
But my 'intuition', as I have informed you already, was 66%, or 2/3 if you like.
Flannel Jesus wrote: Sat Aug 13, 2022 5:14 am If I had one bag with all the grains of sand on a beach in it, and they're all perfect pearlescent spheres, and I had another bag with the grains of sand from another beach, and 1 of them was a perfect pearlescent sphere and the rest of them were grey, and you chose a bag at random, and picked out a single grain of sand at random without looking, and you looked at it and saw that that grain of sand was a perfect pearlescent sphere, you're really telling me that you're still going to say it's 50/50 which bag of sand you chose?
No, not at all.

I asked you, 'Did you read my reply?'

From your response here, you obviously have not yet read my reply. Or, you are so blinded, you can not comprehend what I said and meant.

To me, it is as plain as day that I would not say it is 50/50. This can be clearly seen and proved true from what I have written and said previously.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 5:42 am You know, you can test it yourself. All you need is 11 pennies and 9 dimes. Split them into 2 bags, 1 with 10 pennies and 1 with the rest.

Choose a bag at random, then pick out a coin at random. If it's a penny, record whether you picked the bag full of pennies or whether you picked the one penny out of the bag with 9 dimes. Do that experiment over and over again and find, out of all the times you pull a penny out, what percent of those times you pulled it from the bag full of pennies.

All the theory talk is pointless when a real experiment is both possible and easy to perform.
Are you even aware that what percent you obtain is completely random?

Besides that you have missed that I actually agreed with you. But until you read my replies, you will not see and understand this fact.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 11:27 am Or, think about it like this: when you know one property of something, it can tell you probabilistically about another property of something.

Let's say I have a classroom of 100 kids, and 2 of those kids are black, and both of the black kids have black hair, but only 1 of the other kids has black hair. So 3% have black hair, but all of the black kids have black hair.
There is no such thing as so-called "black kids". So the rest of what you write below is moot.
Flannel Jesus wrote: Sat Aug 13, 2022 11:27 am Now, you're the principal, and there's a kid from my classroom, selected at random waiting outside your office. You know nothing at thi point about who that kid is, other than that he's 1 of the 100 kids. If I ask you, "What's the probability that the kid is one of the black kids?", what's your answer?

And now, I say, "The kid, who was selected at random, happenss to be one of the one with black hair. What' the probability now that the kid is one of the black kids?"

Does the probability change?

If it does, if you think that information changes the probability, then I'm only using the sasme thought process as that in my 50balls per bag example, or my 2 bills per box example. I'm simply usisng one property of an object to tell me probabilistic information about another property of that object.
After you read my replies, and respond to what I have actually written, as well as clarify the actual questions I have posed and asked to you, this experiment is over.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Sat Aug 13, 2022 12:55 pm To me, it is as plain as day that I would not say it is 50/50. This can be clearly seen and proved true from what I have written and said previously.
That's not clear at all to me. I've read it multiple times, it looks like you're still saying it's 50/50 in the case of the blue balls in the bag and still 50/50 in the case of the 2 bills. Can you point me to the bit of your reply that makes it clear you think it isn't 50/50 in the case of the bags of balls?
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 1:28 pm
Age wrote: Sat Aug 13, 2022 12:55 pm To me, it is as plain as day that I would not say it is 50/50. This can be clearly seen and proved true from what I have written and said previously.
That's not clear at all to me. I've read it multiple times, it looks like you're still saying it's 50/50 in the case of the blue balls in the bag and still 50/50 in the case of the 2 bills. Can you point me to the bit of your reply that makes it clear you think it isn't 50/50 in the case of the bags of balls?
'..., or if there were still only two boxes but one box had fifty $100 bills in it and one box with forty nine $1 bills and one $100 bill in it, for example, then, that you are more likely to pull a $100 bill out of the box that is 'full' of $100 bills in it is obviously more likely.'

It is on this page, second post down, and in first sentence of last full paragraph of my post.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Sat Aug 13, 2022 1:42 pm '..., or if there were still only two boxes but one box had fifty $100 bills in it and one box with forty nine $1 bills and one $100 bill in it, for example, then, that you are more likely to pull a $100 bill out of the box that is 'full' of $100 bills in it is obviously more likely.'

It is on this page, second post down, and in first sentence of last full paragraph of my post.
You're confusing the conversation by answering questions that aren't being asked in this part of the conversation, so I still literally have no idea what you think.

If you have 2 bags in front of you, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and you choose a bag blindly, and you reach into it blindly and pull out a ball, and that ball is blue, what is the probability that you chose the bag full of blue balls? Is it 50/50, or is it some other probability?
bobmax
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Re: A fun little probability puzzle for you.

Post by bobmax »

Flannel Jesus wrote: Sat Aug 13, 2022 2:03 pm You're confusing the conversation by answering questions that aren't being asked in this part of the conversation, so I still literally have no idea what you think.

If you have 2 bags in front of you, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and you choose a bag blindly, and you reach into it blindly and pull out a ball, and that ball is blue, what is the probability that you chose the bag full of blue balls? Is it 50/50, or is it some other probability?

Excuse me if I intrude.
I believe that one reason for the underlying misunderstanding is due to considering events that are not independent.

Once the coin tosses a million consecutive "heads", on the next toss the probability of heads is still 50%. Because each event is independent of the other.

Conversely, the probability that the box is the one with two $ 100 is not independent of having already drawn a $ 100 one.
Therefore, those who insist on considering them independent remain on 50%.

In addition to this reason for misunderstanding there is in my opinion another deeper one and it concerns faith in the Truth.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

bobmax wrote: Sat Aug 13, 2022 2:14 pm
Flannel Jesus wrote: Sat Aug 13, 2022 2:03 pm You're confusing the conversation by answering questions that aren't being asked in this part of the conversation, so I still literally have no idea what you think.

If you have 2 bags in front of you, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and you choose a bag blindly, and you reach into it blindly and pull out a ball, and that ball is blue, what is the probability that you chose the bag full of blue balls? Is it 50/50, or is it some other probability?

Excuse me if I intrude.
I believe that one reason for the underlying misunderstanding is due to considering events that are not independent.

Once the coin tosses a million consecutive "heads", on the next toss the probability of heads is still 50%. Because each event is independent of the other.

Conversely, the probability that the box is the one with two $ 100 is not independent of having already drawn a $ 100 one.
Therefore, those who insist on considering them independent remain on 50%.

In addition to this reason for misunderstanding there is in my opinion another deeper one and it concerns faith in the Truth.
They're clearly not independent though. The probability of one thing happening changes drastically if the other thing happened, which is entirely unlike a coin flip
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