A fun little probability puzzle for you.

What is the basis for reason? And mathematics?

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bobmax
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Re: A fun little probability puzzle for you.

Post by bobmax »

Flannel Jesus wrote: Sat Aug 13, 2022 2:16 pm 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
But this evidence is not seen.

How is it possible not to see it?

In my opinion this is the question, beyond the statistics.

The fact is that for even the slightest real rational communication to take place, both parties must be animated by faith in the Truth.
If this faith is lacking, even in only one of the parts at stake, rational communication is fictitious.

Maybe you can still be able to communicate, but through channels other than rationality.

Your dedication is admirable.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Actually I think everyone here agrees that these two events in question : selecting a bag, and then selecting a ball (or selecting a box, and then a bill) : are unlike a pair of conflips. A pair of coin flips has two way mutual independence. The scenario of the balls in bags, at the very least, has a one way dependence (and I'm arguing a two way dependence), and everyone agrees that it at least has a one way dependence.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 2:03 pm
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.
What 'part' of the conversation are you referring to here?
Flannel Jesus wrote: Sat Aug 13, 2022 2:03 pm 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?

For the third time;

'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.'

Which literally means:
If I have 2 bags in front of me, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and I choose a bag blindly, and I reach into it blindly and pull out a ball, and that ball is blue, then what the probability that I chose the bag full of blue balls is 50/50. This is because there was only 2 things to choose from.

IT IS OBVIOUSLY MORE LIKELY, however, as I explained above, that if I chose the bag with the 50 blue balls in it, then I would pull a blue ball out of it than a red ball.

Knowing what I pulled out does not change what the actual odds were when I chose the two bags. That will always remain 50/50. To say otherwise would be like 'trying to' argue that if I toss a coin 49 times, for example, and that each one of those tosses was a head, then this means that there will be more probabilities that the next toss will be a tail. It does not work like that.

The probability that I picked the bag with all blue balls will always remain 50/50, until proof is shown otherwise. Which, by the way, will only take the picking of two balls out of the bag.

What do you think is the probability that I chose the bag full of blue balls, in your example above?
Age
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Re: A fun little probability puzzle for you.

Post by Age »

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.
Will you explain more in relation to what 'faith in the Truth' consists of exactly?
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Sat Aug 13, 2022 2:49 pm
'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.'

Which literally means:
If I have 2 bags in front of me, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and I choose a bag blindly, and I reach into it blindly and pull out a ball, and that ball is blue, then what the probability that I chose the bag full of blue balls is 50/50. This is because there was only 2 things to choose from.
No, the first paragraph does not literally mean the second paragraph. That's... not true at all. Those are two entirely different statements. I can't see any way to interpret that where those two paragraphs literally mean the same thing.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 2:56 pm
Age wrote: Sat Aug 13, 2022 2:49 pm
'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.'

Which literally means:
If I have 2 bags in front of me, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and I choose a bag blindly, and I reach into it blindly and pull out a ball, and that ball is blue, then what the probability that I chose the bag full of blue balls is 50/50. This is because there was only 2 things to choose from.
No, the first paragraph does not literally mean the second paragraph. That's... not true at all. Those are two entirely different statements. I can't see any way to interpret that where those two paragraphs literally mean the same thing.
You are exactly right here.

After I changed the words in the second paragraph I forgot to remove the, "Which literally means:" sentence.

My apologies.

But if I did move those three words down to the next sentence, and removed the, "however, as I explained above," words from that sentence, then it would follow, and be true, right?
Last edited by Age on Sat Aug 13, 2022 3:04 pm, edited 1 time in total.
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
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.
Which brings me back to this.

If you think it's 50/50 in the bag example, then it's consistent for you to think it's 50/50 in the grains of sand example. So how is it "plain as day"? It's not plain as day. I don't see how you wouldn't think it's 50/50 with the bags of sand
bobmax
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Re: A fun little probability puzzle for you.

Post by bobmax »

Flannel Jesus wrote: Sat Aug 13, 2022 2:35 pm Actually I think everyone here agrees that these two events in question : selecting a bag, and then selecting a ball (or selecting a box, and then a bill) : are unlike a pair of conflips. A pair of coin flips has two way mutual independence. The scenario of the balls in bags, at the very least, has a one way dependence (and I'm arguing a two way dependence), and everyone agrees that it at least has a one way dependence.
I don't think everyone sees dependence.

The 50% response may come from having seen the link, however incomplete.
But the same 50% response can come from excluding any relationship.

This second motivation may derive from the paroxysmal perception of chance.

Perception that has its own raison d'etre... But that should be managed by taking a step back, not a step forward.

When pure intuition takes over, perhaps deep truths are grasped, but without faith you risk being crushed.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 3:02 pm
Age wrote: Sat Aug 13, 2022 12:55 pm
Flannel Jesus wrote: Sat Aug 13, 2022 5:14 am

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.
Which brings me back to this.

If you think it's 50/50 in the bag example, then it's consistent for you to think it's 50/50 in the grains of sand example. So how is it "plain as day"? It's not plain as day. I don't see how you wouldn't think it's 50/50 with the bags of sand
You keep missing the point.

I do not 'think' this.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

bobmax wrote: Sat Aug 13, 2022 3:04 pm
Flannel Jesus wrote: Sat Aug 13, 2022 2:35 pm Actually I think everyone here agrees that these two events in question : selecting a bag, and then selecting a ball (or selecting a box, and then a bill) : are unlike a pair of conflips. A pair of coin flips has two way mutual independence. The scenario of the balls in bags, at the very least, has a one way dependence (and I'm arguing a two way dependence), and everyone agrees that it at least has a one way dependence.
I don't think everyone sees dependence.

The 50% response may come from having seen the link, however incomplete.
But the same 50% response can come from excluding any relationship.

This second motivation may derive from the paroxysmal perception of chance.

Perception that has its own raison d'etre... But that should be managed by taking a step back, not a step forward.
bobmax wrote: Sat Aug 13, 2022 3:04 pm When pure intuition takes over, perhaps deep truths are grasped, but without faith you risk being crushed.
This is absolute Truth.

This is because of what 'Intuition' is, and where 'It' comes from, exactly.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

So what's different then? The two situations are entirely parallel.

Bag 1 with 50 blue balls
Bag 2 with 1 blue 49 red
You pick a bag, pick a ball, see that the ball is blue, and say "it's 50/50 that I chose the bag full of blue balls"

Compared to

Bag 1 with 1,000,000 grains of pearlescent sand
Bag 2 with 1 grain of pearlescent sand, 999,999 grains of grey sand
You pick a bag, pick a grain out, see that the grain is pearlescent,
So being entirely consistent with the blue balls example, I can't see why you would not say "it's 50/50 that I chose the bag full of pearlescent sand"

Whats different?
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 3:08 pm So what's different then? The two situations are entirely parallel.

Bag 1 with 50 blue balls
Bag 2 with 1 blue 49 red
You pick a bag, pick a ball, see that the ball is blue, and say "it's 50/50 that I chose the bag full of blue balls"
But I would not say this.

Why would you assume and say that I would?

Just so you are aware, I choose and use my words very specifically.

Not always correctly, as evidenced and proved above, but very specifically.
Flannel Jesus wrote: Sat Aug 13, 2022 3:08 pm Compared to

Bag 1 with 1,000,000 grains of pearlescent sand
Bag 2 with 1 grain of pearlescent sand, 999,999 grains of grey sand
You pick a bag, pick a grain out, see that the grain is pearlescent,
So being entirely consistent with the blue balls example, I can't see why you would not say "it's 50/50 that I chose the bag full of pearlescent sand"
Okay.
Flannel Jesus wrote: Sat Aug 13, 2022 3:08 pm Whats different?
Also, if I recall correctly you wanted me to change the way I wrote here, which I am doing. I also asked you to answer every question I ask you for clarity, which you were doing, but have now stopped doing.

I asked you, among other questions, 'What do you think is the probability that I chose the bag full of blue balls, in your example above?'
The words and numbers you used here.
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Sat Aug 13, 2022 3:27 pm
Flannel Jesus wrote: Sat Aug 13, 2022 3:08 pm So what's different then? The two situations are entirely parallel.

Bag 1 with 50 blue balls
Bag 2 with 1 blue 49 red
You pick a bag, pick a ball, see that the ball is blue, and say "it's 50/50 that I chose the bag full of blue balls"
But I would not say this.

Why would you assume and say that I would?
I don't think I am assuming. I think I'm just paraphrasing what you wrote here:
If I have 2 bags in front of me, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and I choose a bag blindly, and I reach into it blindly and pull out a ball, and that ball is blue, then what the probability that I chose the bag full of blue balls is 50/50
I don't answer all your questions every time because I don't like confusing conversations with too many threads. I like to get clarity, then move on, then get clarity, then move on. If things are unclear, I don't want to keep moving forward until they become clear again. Clarity is central to me. If things are not clear, I'm going to focus on the parts that are not clear, until they are.

Right now, what you think is not clear. First you say "If I have 2 bags in front of me, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and I choose a bag blindly, and I reach into it blindly and pull out a ball, and that ball is blue, then what the probability that I chose the bag full of blue balls is 50/50". Then I paraphrase that in a way I think is very much the same in meaning, and you say "I would not say this", so I genuinely have no idea why you wouldn't say it, or what you actually think at this point. I want to get clarity.
Age
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Re: A fun little probability puzzle for you.

Post by Age »

Flannel Jesus wrote: Sat Aug 13, 2022 3:31 pm
Age wrote: Sat Aug 13, 2022 3:27 pm
Flannel Jesus wrote: Sat Aug 13, 2022 3:08 pm So what's different then? The two situations are entirely parallel.

Bag 1 with 50 blue balls
Bag 2 with 1 blue 49 red
You pick a bag, pick a ball, see that the ball is blue, and say "it's 50/50 that I chose the bag full of blue balls"
But I would not say this.

Why would you assume and say that I would?
I don't think I am assuming. I think I'm just paraphrasing what you wrote here:
Well you are not. As can be clearly seen and proved by the actual words that have been used.
Flannel Jesus wrote: Sat Aug 13, 2022 3:31 pm
If I have 2 bags in front of me, and one has 50 blue balls, and the other has 1 blue ball and 49 red balls, and I choose a bag blindly, and I reach into it blindly and pull out a ball, and that ball is blue, then what the probability that I chose the bag full of blue balls is 50/50
I don't answer all your questions every time because I don't like confusing conversations with too many threads.
How can you clarifying a question, asked for clarification, be confusing conversations?

To me, you would be clearing things up and not confusing at all.
Flannel Jesus wrote: Sat Aug 13, 2022 3:31 pm I like to get clarity, then move on, then get clarity, then move on.
Which is exactly what I seek to do when I ask you a question. for clarity. But if you never answer that question, and just keep moving on, then what you are doing is either being deceitful or deceptive, or just allowing confusion to grow.
Flannel Jesus wrote: Sat Aug 13, 2022 3:31 pm If things are unclear, I don't want to keep moving forward until they become clear again.
LOL What do you think I am doing when I ask you a question, for clarification?
Flannel Jesus wrote: Sat Aug 13, 2022 3:31 pm Clarity is central to me. If things are not clear, I'm going to focus on the parts that are not clear, until they are.
And how exactly do you focus on the parts that are not clear, until they are?

In other words how do you obtain clarity on 'that', which is not yet clear?
Flannel Jesus
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Re: A fun little probability puzzle for you.

Post by Flannel Jesus »

Age wrote: Sat Aug 13, 2022 3:40 pm
Flannel Jesus wrote: Sat Aug 13, 2022 3:31 pm
Age wrote: Sat Aug 13, 2022 3:27 pm

But I would not say this.

Why would you assume and say that I would?
I don't think I am assuming. I think I'm just paraphrasing what you wrote here:
Well you are not. As can be clearly seen and proved by the actual words that have been used.
This is turning into a silly game. I'm not interested in the silly game. If you think my paraphrasing is incorrect, you can explain why it's incorrect. But instead of doing that, you want to start silly games.

My paraphrasing was honest, so if you think there's something incorrect about it, point it out or end the conversation.
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