A fun little probability puzzle for you.

[Flannel Jesus]

In your opinion, any time there are two options it's a 50/50?

[Age]

In your opinion, any time there are two options it's a 50/50?

If the two options are based on or from two things ONLY.

Which, in YOUR EXAMPLE, there are ONLY two things, OBVIOUSLY.

[Flannel Jesus]

Right, okay, very rarely do I meet someone with such a unique view on probabilities, but it has happened before.

So if I put 100 balls into a bag, and 99 of them were blue, and 1 was red, and shuffled them about and asked you to pick one without looking, you think the probability of picking the red one is 50/50? Because there's are two options? Have I understood you correctly?

[Skepdick]

In your opinion, any time there are two options it's a 50/50?

It depends on what you are measuring - subject to choice.

In my opinion any time there are two options the odds are a free variable. You can choose to condition this variable upon prior knowledge, or you can choose to condition this variable upon the principle of maximym entropy e.g zero knowledge.

I had the option of tea or coffee this morning. Should I condition my choosing on my prior choices; or should I choose as if 50/50?

[Skepdick]

Right, okay, very rarely do I meet someone with such a unique view on probabilities, but it has happened before.

So if I put 100 balls into a bag, and 99 of them were blue, and 1 was red, and shuffled them about and asked you to pick one without looking, you think the probability of picking the red one is 50/50? Because there's are two options? Have I understood you correctly?

It depends on what you know - it depends on how you condition your prior!

If I told you that I put some balls in a bag.
Some of them are red and some of them are blue.

What's your probability of picking up a red one? Knowing THAT you don't know what prior would you choose for your first estimate?

And what happens to the experiment if I removed the "without looking" condition?!?

[Age]

Right, okay, very rarely do I meet someone with such a unique view on probabilities, but it has happened before.

So if I put 100 balls into a bag, and 99 of them were blue, and 1 was red, and shuffled them about and asked you to pick one without looking, you think the probability of picking the red one is 50/50? Because there's are two options? Have I understood you correctly?

You REALLY do NOT READ and UNDERSTAND what I ACTUALLY WRITE and SAY, do you, even though MY WORDS are CLEARLY WRITTEN here for ALL to LOOK AT and SEE?

I CLEARLY WROTE:
If the two options are based on or from two things ONLY.

Which, in YOUR EXAMPLE, there are ONLY two things, OBVIOUSLY.

Now, in the FIRST line, or sentence, I CLEARLY SAID and STATED; IF 'the two options' ARE 'based on or from TWO 'things' ONLY.

Which, OBVIOUSLY MEANS, in YOUR EXAMPLE here with '100 hundred balls' this is NOT 'two things', ONLY.

Can you SEE, GRASP, and UNDERSTAND the DIFFERENCE here?

If no, then this WILL take MUCH LONGER than FIRST ENVISIONED.

[Flannel Jesus]

But there aren't 2 things only in the original question either. There are 3.

Once you've picked the first $100, there's still 2 more $100s and a $1

[Skepdick]

But there aren't 2 things only in the original question either. There are 3.

Once you've picked the first $100, there's still 2 more $100s and a $1

And what happens to your thought experiment if you proceed to make two more picks and end up 2x $1 notes?

Which beliefs should you adjust, and how should you adjust them?

[Age]

But there aren't 2 things only in the original question either. There are 3.

LOL This is the VERY thing that I have been POINTING OUT and SHOWING. It is 'this' that I have been continually INFORMING you that you are MISSING.

There are NOT 3, DIFFERENT, things. There are ONLY 2, DIFFERENT, things.

OF COURSE, there are 3 things, but they are NOT DIFFERENT things.

Once you've picked the first $100, there's still 2 more $100s and a $1

LOL

There is ONLY ONE more $100 bill, and ONE $1 bill, although there are THREE different bills or pieces of paper.

WHEN, and IF, you START to ENVISION the 'pieces of paper' being 'colored', then you can SEE HOW there is ONLY ONE MORE $100 bill.

Or, if you ENVISION the number or denominations on the 'bills' ('pieces of paper) as being colors.

There are MANY ways to EXPLAIN this.

Imagine there are now 3 balls remaining, after you removed 1 ball. The ball you removed was a blue ball, and the 3 remainings balls are 2 blue and 1 red.

There is now only 2 options left in the box you chose from. That is either a blue ball or a red ball. And, if I asked you what is the probability that the remaining ball is a blue or a red one, then what would you say? 50% chance or still 66% chance?

There is ANOTHER, also very simple and easy way to explain and SHOW this, if this way STILL does NOT work for you.

[Flannel Jesus]

But there aren't 2 things only in the original question either. There are 3.

LOL This is the VERY thing that I have been POINTING OUT and SHOWING. It is 'this' that I have been continually INFORMING you that you are MISSING.

There are NOT 3, DIFFERENT, things. There are ONLY 2, DIFFERENT, things.

OF COURSE, there are 3 things, but they are NOT DIFFERENT things.

Once you've picked the first $100, there's still 2 more $100s and a $1

LOL

There is ONLY ONE more $100 bill, and ONE $1 bill, although there are THREE different bills or pieces of paper.

Okay, so in my example of 100 balls, why don't you take the same approach?

[Age]

But there aren't 2 things only in the original question either. There are 3.

LOL This is the VERY thing that I have been POINTING OUT and SHOWING. It is 'this' that I have been continually INFORMING you that you are MISSING.

There are NOT 3, DIFFERENT, things. There are ONLY 2, DIFFERENT, things.

OF COURSE, there are 3 things, but they are NOT DIFFERENT things.

Once you've picked the first $100, there's still 2 more $100s and a $1

LOL

There is ONLY ONE more $100 bill, and ONE $1 bill, although there are THREE different bills or pieces of paper.

Okay, so in my example of 100 balls, why don't you take the same approach?

BECAUSE that example IS DIFFERENT.

[Age]

In your first example there are ONLY 2 things. In your second example there are 100 things.

[Flannel Jesus]

Would it still be different if I added another box with 2x100? So now there's 3 boxes, and 2 of them have 2 100s? Is it still 50/50 because there's only 2 options, or do you start counting the extra 100s then?

[Age]

Would it still be different if I added another box with 2x100? So now there's 3 boxes, and 2 of them have 2 100s? Is it still 50/50 because there's only 2 options, or do you start counting the extra 100s then?

On first, and very quick, thought there will always only ever be a 'probability' of 50/50.

This is because there will always only ever be 1 $100 bill and 1 $1 bill, remaining in that one box.

The misleading, or 'deception', is the brain thinks of the $100 bills being different, when really they are not. Sure the bill is a different piece of paper but it will always still be a $100.

Imagine the $100 as the color 'red', the $1 as the 'blue' color, and the 'bill' as the 'ball'. Does this help?

If you put 2 red balls into a box, and 1 red ball in a box with a blue ball. Pick one box, and pick a red ball out, the chance that there is a red ball remaining in that box will be 50%. It could only ever be either a red ball or a blue ball in there.

For some reason, which I have not even begun to think of yet, the brain pictures or imagines $100 bills as being DIFFERENT, whereas the brain thinks of red balls being THE SAME.

[Flannel Jesus]

My brain thinks of them exactly the same. I don't treat the balls differently from the money