A fun little probability puzzle for you.

[Age]

I'll pick the one on my left.

Okay.

What was the probability of picking that one?

And why?

What is the probability that there is a $100 bill in it?

And why?

What is the probability that there is a $1 bill in it?

And why?

[Flannel Jesus]

I'll pick the one on my left.

Okay.

What was the probability of picking that one?

And why?

From my perspective, probably something like 80%. If given a choice and all things are equal, I usually go left.

What is the probability that there is a $100 bill in it?

And why?

100%, you said both boxes have at least 1 $100 in them.

What is the probability that there is a $1 bill in it?

And why?

50%, since one of the two boxes has a $1 in it.

[Age]

I'll pick the one on my left.

Okay.

What was the probability of picking that one?

And why?

From my perspective, probably something like 80%. If given a choice and all things are equal, I usually go left.

What is the probability that there is a $100 bill in it?

And why?

100%, you said both boxes have at least 1 $100 in them.

What is the probability that there is a $1 bill in it?

And why?

50%, since one of the two boxes has a $1 in it.

Okay, now in that one box only that you have chosen, without looking, you pull one bill out of it and it is a $100 bill.

What was the probability that that would happen?

And why?

[Flannel Jesus]

3/4, because 3 of the 4 possible bills are $100

[Age]

3/4, because 3 of the 4 possible bills are $100

Okay, now with that one box only and with that one $100 bill only that you pulled out of that box, what is the probability that you chose the box with two $100 bills in it?

And why?

[Flannel Jesus]

3/4, because 3 of the 4 possible bills are $100

Okay, now with that one box only and with that one $100 bill only that you pulled out of that box, what is the probability that you chose the box with two $100 bills in it?

And why?

2/3.

There were 3 ways to choose $100 to begin with (the 3 in 3/4), and 2 of those three ways were from the box with 2x100

[Age]

3/4, because 3 of the 4 possible bills are $100

Okay, now with that one box only and with that one $100 bill only that you pulled out of that box, what is the probability that you chose the box with two $100 bills in it?

And why?

2/3.

There were 3 ways to choose $100 to begin with (the 3 in 3/4), and 2 of those three ways were from the box with 2x100

But there were only two boxes to choose from to begin with. To begin with there were only boxes to choose from.


So, how exactly were there 3 ways to choose to begin with?

[Flannel Jesus]

You asked me "Okay, now with that one box only and with that one $100 bill only that you pulled out of that box, what is the probability that you chose the box with two $100 bills in it?"

There's 4 ways to choose a bill at the start.

1. Choose 100+1 box, choose 1
2. Choose 100+1 box, choose 100
3. Choose 100+100 box, choose the first 100
4. Choose 100+100 box, choose the second 100


So there's 4 possible routes of choosing a box and choosing a bill, and 3 of them end up with you having chosen a $100, and 2 of those 3 routes are from the 100+100 box

[Age]

You asked me "Okay, now with that one box only and with that one $100 bill only that you pulled out of that box, what is the probability that you chose the box with two $100 bills in it?"

There's 4 ways to choose a bill at the start.

1. Choose 100+1 box, choose 1
2. Choose 100+1 box, choose 100
3. Choose 100+100 box, choose the first 100
4. Choose 100+100 box, choose the second 100


So there's 4 possible routes of choosing a box and choosing a bill, and 3 of them end up with you having chosen a $100, and 2 of those 3 routes are from the 100+100 box

The first part is right.

But I also asked you, And why?

You are here not answering the actual question I posed for you, and asked you.

Anyway, now with that one box only that you have chosen, and before you pull anything out of it, what is the probability that you chose the box with two $100 bills in it?

And why?

[Flannel Jesus]

The first part is right.

But I also asked you, And why?

You are here not answering the actual question I posed for you, and asked you.

Anyway, now with that one box only that you have chosen, and before you pull anything out of it, what is the probability that you chose the box with two $100 bills in it?

And why?

I'm trying to answer the question, I can't control if you find my answer satisfying. I feel like I answered why I think that.

Before you pull out the first note, naturally it's 50/50, for the obvious reasons

[Age]

The first part is right.

But I also asked you, And why?

You are here not answering the actual question I posed for you, and asked you.

Anyway, now with that one box only that you have chosen, and before you pull anything out of it, what is the probability that you chose the box with two $100 bills in it?

And why?

I'm trying to answer the question, I can't control if you find my answer satisfying. I feel like I answered why I think that.

Before you pull out the first note, naturally it's 50/50, for the obvious reasons

Okay.

So, as I asked from the beginning it is 50%.

Now, why when you pull out a $100 bill do you say it then becomes 66%?

[Flannel Jesus]

So, as I asked from the beginning it is 50%.

Now, why when you pull out a $100 bill do you say it then becomes 66%?

Yes, that's right. 2/3 to be precise, approximately 66%.

[Age]

So, as I asked from the beginning it is 50%.

Now, why when you pull out a $100 bill do you say it then becomes 66%?

Yes, that's right. 2/3 to be precise, approximately 66%.

How come you could answer all of the other questions I asked you for clarity, but you did not answer the above one here?

If I recall correctly in the other thread you wanted me to agree to writing a particular way in this thread, which I did, and then I asked you if you would agree to answering all of the actual questions that I asked you here in this thread, which you agreed to.

Now, if, as you say, the probability is 50/50 before you pull out one $100 bill, then why after you pull out one $100 bill the probability, supposedly, changes to 2/3?

[Flannel Jesus]

If there's a question I miss that you think is important for me to answer, feel free to point me to it again. It's sometimes hard to maintain a clean conversation where there's many questions in a single post. Clarity is important to me, so I often focus on the questions that I clearly understand and can clearly answer.

Now, if, as you say, the probability is 50/50 before you pull out one $100 bill, then why after you pull out one $100 bill the probability, supposedly, changes to 2/3?

Because there's 3 ways for you to have ended up with a $100 bill in your hand, and 2 of those ways are from the 2*100 box.

Probabilities may change when you receive new information. What's the probability that I have black hair, with what you know about me now? A quick Google tells me that 75-85% of the world has black hair, BUT we're speaking in English on a philosophy forum, so you might assume I live in a Western or European country, so maybe you bring that number down a bit, maybe you guess that it's about 60%, or possibly lower.

Now what if I told you I'm a native subsaharan African? What's the probability that I have black hair now? It's increased. The vast majority of native subsaharan Africans have natural black hair. Much more than 60% I'm sure.

New information can change probabilities.

[Age]

If there's a question I miss that you think is important for me to answer, feel free to point me to it again. It's sometimes hard to maintain a clean conversation where there's many questions in a single post. Clarity is important to me, so I often focus on the questions that I clearly understand and can clearly answer.

Absolutely every sentence with a question mark at the end is a question that is important for you to answer. The very reason I pose and ask questions here, for clarification, is because I find the answer/s, if given, will be very important.

Now, if, as you say, the probability is 50/50 before you pull out one $100 bill, then why after you pull out one $100 bill the probability, supposedly, changes to 2/3?

Because there's 3 ways for you to have ended up with a $100 bill in your hand, and 2 of those ways are from the 2*100 box.

Probabilities may change when you receive new information.

They may, but they also may not.

What's the probability that I have black hair, with what you know about me now? A quick Google tells me that 75-85% of the world has black hair, BUT we're speaking in English on a philosophy forum, so you might assume I live in a Western or European country, so maybe you bring that number down a bit, maybe you guess that it's about 60%, or possibly lower.

This here is a prime example of why I do not like to assume absolutely any thing at all.

Now what if I told you I'm a native subsaharan African? What's the probability that I have black hair now? It's increased. The vast majority of native subsaharan Africans have natural black hair. Much more than 60% I'm sure.

Are you purposely 'trying to' deflect?

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?

New information can change probabilities.

But, obviously, not necessarily so, correct?