Expanding on the logic riddle:

[Fort Fun Indiana]

The first card I chose is on your left. I turn over the first card. It is red.

You mean, the first card *I* drew from the deck and laid face-down in front of you, to your left.

You only know if the.first card I drew is on your left or your right in cases 1 and 2.

In cases 3 and 4 you do not have this information.

This matters.

 

[Toddsterpatriot]

You mean, the first card *I* drew from the deck and laid face-down in front of you, to your left.

You only know if the.first card I drew is on your left or your right in cases 1 and 2.

In cases 3 and 4 you do not have this information.

This matters.

You mean, the first card *I* drew from the deck and laid faace-down in front of you, to your left.

The first card, which you flipped over, and said was red.

You only know if the.first card I drew is on your left or your right in cases 1 and 2.

In both cases, it was red.

In cases 3 and 4 you do not have this information.

I don't need to know which one you drew first, I only need to know you flip over a red card.

 

[Fort Fun Indiana]

I don't need to know which one you drew first

Actually, you do.

 

[Toddsterpatriot]

Actually, you do.

Doesn't matter when you draw them or where you put them.
You flip one over, it's red, the odds the next one is red.....50%.

 

[Fort Fun Indiana]

Doesn't matter when you draw them or where you put them.
You flip one over, it's red, the odds the next one is red.....50%.

Wrong again.

 

[Fort Fun Indiana]

Why is it I care?

Brainercise!

 

[Fort Fun Indiana]

Toddsterpatriot

Try it this way:

I drew two cards. I tell you at least one is red.

What is the probability both are red?

1/3

 

[Toddsterpatriot]

Wrong again.

Three unknown cards drawn at random....what are the odds all three are red?

0.5*0.5*0.5= 0.125, 1 chance in 8.

Flip over the first card, it's red. What are the odds all three cards are red, 1.0*0.5*0.5=0.25, 1 in 4.

Flip over the second card, it's red. What are the odds all three cards are red, 1.0*1.0*0.5=0.5, 1 in 2.

Need any more?

 

[Fort Fun Indiana]

Three unknown cards drawn at random....what are the odds all three are red?

0.5*0.5*0.5= 0.125, 1 chance in 8.

Flip over the first card, it's red. What are the odds all three cards are red, 1.0*0.5*0.5=0.25, 1 in 4.

Flip over the second card, it's red. What are the odds all three cards are red, 1.0*1.0*0.5=0.5, 1 in 2.

Need any more?

You should slow down. You have yet to get the riddle correct with two cards.

Let's try again.

I pull two cards. I tell you at least one of them is red.

What is the probability both are red?

1/3.

Get it yet? Do you understand how this is the equivalent of scenarios 3 and 4?

 

[Toddsterpatriot]

You should slow down. You have yet to get the riddle correct with two cards.

Let's try again.

I pull two cards. I tell you at least one of them is red.

What is the probability both are red?

1/3.

Get it yet? Do you understand how this is the equivalent of scenarios 3 and 4?

I'm trying to help you. It's not working, eh?

I pull two cards. I tell you at least one of them is red.

Almost.

You pull two cards, the first one you flip is red.

Get it yet? Do you understand how this is the equivalent of scenarios 3 and 4?

3) I pull one card, then another. Before I lay the two cards down face-down in front of you, I shuffle them behind my back. I lay them face-down in front of you, and I turn over the card to your left. It is red.

What is the probability the card on the right is also red?
.................

4) I pull one card, then another. Before I lay the two cards down face-down in front of you, I shuffle them behind my back. I lay them face-down in front of you, and I turn over the card to your right. It is red.

It's not equivalent.

 

[Fort Fun Indiana]

Flip over the first card, it's red.

I'm trying to help you. It's not working, eh?

I pull two cards. I tell you at least one of them is red.

Almost.

You pull two cards, the first one you flip is red.

Get it yet? Do you understand how this is the equivalent of scenarios 3 and 4?

3) I pull one card, then another. Before I lay the two cards down face-down in front of you, I shuffle them behind my back. I lay them face-down in front of you, and I turn over the card to your left. It is red.

What is the probability the card on the right is also red?
.................

4) I pull one card, then another. Before I lay the two cards down face-down in front of you, I shuffle them behind my back. I lay them face-down in front of you, and I turn over the card to your right. It is red.

It's not equivalent.

Todd, I assure you that you are wrong. As I would expect most people to be, when first encountering this riddle.

If you only know at least one of my two cards is red, you only know I hold one of three, equally likely permutations:

BR
RB
RR

What is the probability the other card is black?

2/3

And yes, this is equivalent to scenarios 3 and 4. In those scenarios, the only information revealed to you is that at least one card is red.

In scenarios 1 and 2, you have more information. You know which card was drawn first, and which was drawn second.

In revealing the first-drawn card is red, you reduce the number of equally possibly permutations to TWO:

RB
RR

You know know I hold one of these two, equally likely permutations.

 

[Toddsterpatriot]

Todd, I assure you that you are wrong. As I would expect most people to be, when first encountering this riddle.

If you only know at least one of my two cards is red, you only know I hold one of three, equally likely permutations:

BR
RB
RR

What is the probability the other card is black?

2/3

And yes, this is equivalent to scenarios 3 and 4. In those scenarios, the only information revealed to you is that at least one card is red.

In scenarios 1 and 2, you have more information.

If you only know at least one of my two cards is red, you only know I hold one of three, equally likely permutations:

BR
RB
RR

You can keep changing the scenario, won't make your original less wrong.

I have a deck of cards. Half are red, half are black. Every time I pull one out, it is magically replaced in the deck, and the deck is re-shuffled. FOUR scenarios in this riddle:

1) I pull one card, then another, laying them face down in front of you. The first card I chose is on your left.

I turn over the first card. It is red. What is the probability the other card is also red?

You flipped over the one on my left, the first card, reading left to right.

BR
RB
RR

In your changed scenario, the top permutation is impossible.
You now have two possibilities.

RB
RR

In scenarios 1 and 2, you have more information.

In all the scenarios, the information I have is you flip a red card.

 

[Fort Fun Indiana]

You can keep changing the scenario

I have not changed it one single time. That should be a strong clue to you that it is you who does not understand. Which you then immediately prove:

1) I pull one card, then another, laying them face down in front of you. The first card I chose is on your left.

I turn over the first card. It is red. What is the probability the other card is also red?

You flipped over the one on my left, the first card, reading left to right.

BR
RB
RR

That is wrong. In scenario 1, as you know the first card I chose from the deck is on your left, flipping it to reveal a red card leaves only TWO, equally possible permutations:

RB
RR

You can no longer consider the "BR" permutation, as we have ruled it out. In this case, the probability the other card is also red is 50%.

 

[Toddsterpatriot]

I have not changed it one single time. That should be a strong clue to you that it is you who does not understand. Which you then immediately prove:


That is wrong. As you know the first card I chose from the deck is on your left, flipping it to reveal a red card leaves only TWO, equally possible permutations:

RB
RR

You can no longer consider the "BR" permutation, as we have ruled it out. In this case, the probability the other card is also red is 50%.

Like I said, 50% chance the second card is red.

Glad you realize your error.

 

[Toddsterpatriot]

You should slow down. You have yet to get the riddle correct with two cards.

Let's try again.

I pull two cards. I tell you at least one of them is red.

What is the probability both are red?

1/3.

Get it yet? Do you understand how this is the equivalent of scenarios 3 and 4?

Your post #22. You didn't tell me, before you flipped a card, that at least one is red.

You flipped a red one, 50% chance the unflipped one is also red.

Get it yet?

 

[Fort Fun Indiana]

Like I said, 50% chance the second card is red.

Glad you realize your error.

In scenarios 1 and 2. Yes, that is correct, though you just arrived at the answer for the wrong reasons.

In scenarios 3 and 4, it is 1/3.

The scenarios have not changed, and the answers have not changed. And you clearly still do not understand the fundamental ideas at work, here.

 

[Fort Fun Indiana]

Your post #22. You didn't tell me, before you flipped a card, that at least one is red.

A kind of silly comment. Flipping one and revealing that it is red IS revealing to you that "at least one card is red".

Simply telling you at least one card is red is exactly the same as flipping one card to reveal a red card, in scenarios 3 and 4.

But not in scenarios 1 and 2. Because, in those scenarios, you have more information.

 

[Fort Fun Indiana]

Toddsterpatriot I know you can get this.

 

[Toddsterpatriot]

A kind of silly comment. Flipping one and revealing that it is red IS revealing to you that "at least one card is red".

Simply telling you at least one card is red is exactly the same as flipping one card to reveal a red card, in scenarios 3 and 4.

But not in scenarios 1 and 2. Because, in those scenarios, you have more information.

A kind of silly comment. Flipping one and revealing that it is red IS revealing to you that "at least one card is red".

You revealed the first card you flip is red. Only two choices for the second card.

Simply telling you at least one card is red

In post #22, you didn't say at least one card was red, you simply flipped a red card.

But not in scenarios 1 and 2. Because, in those scenarios, you have more information.

How is the info in those scenarios different? Shuffle or not, the first flipped is red.

 

[Fort Fun Indiana]

In post #22, you didn't say at least one card was red, you simply flipped a red card.

Correct. I was restating scenarios 3 and 4 another way, when I said "it is revealed to you that at least one card is red". Nothing about the scenarios themselves changed.

Third time:

Telling you "at least one card is red" is the equivalent of flipping one card to reveal a red card, I'm scenarios 3 and 4.

But not in scenarios 1 and 2.