Expanding on the logic riddle:

[Fort Fun Indiana]

Now you are changing the problem to try to prove you are correct.

No, that's what I originally said. You must have missed it.

I am not even talking about "the problem" in the OP. I am explaining why I used "infinite deck", instead of "with replacement".

So, let's roll with, "With replacement". Will re-word the OP next, just for you and Toddsterpatriot and Dogmaphobe .

 

[Fort Fun Indiana]

Restating the riddle in the OP:

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?
.........

2) 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 second card (the one on your right). It is red. What is the probability the other card is red?

...........

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.

What is the probability the card on the left is also red?

 

[Fort Fun Indiana]

You can't ask a question about an infinite set, then use a finite set of 100 to prove your point.

We definitely can, by using operations on sets. For example, 'union'.

Do you know anything about cardinality? Some infinite sets have more members than other infinite sets. Go check. It's a starting point to understand the construction of infinite sets.

 

[Winco]

So, let's roll with, "With replacement". Will re-word the OP next, just for you and @Toddsterpatriot and @Dogmaphobe .

Ok, if this is a 'riddle' and a play on words, then yup, you got me, I don't see the riddle part.

In the case you just suggested in post #22, is it an 'infinite deck' as you suggested or is this NEW post #22 a 52 card deck. If the card is magically replaced in the deck, before you draw again, then it wouldn't matter.

If this is purely mathematical and you just used the word riddle for some reason, then it is 1/2 for all three cases.

Every time I pull one out, it is magically replaced in the deck. THREE scenarios in this riddle:

If the card you pulled magically is replaced in the deck, then the deck being pulled from would always be from the original deck.

 

[Toddsterpatriot]

I have an infinite deck of cards. Half are red, half are black.

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?
.........

2) I turn over the second card, first. It is red. What is the probability the other card is red?

...........

3) Before I lay the two cards down, I shuffle them behind my back. I lay them 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?

You didn't replace, reshuffle, or start from scratch in the original.

1) You pulled two cards. You flip the left one, it's red. 50% chance the right one is red.

2) Same two cards, in the same places, you flip the right one, it's also red.
You already said the left one was red, 100% chance the left one is red.

3) You shuffle the same two red cards and place them in front of me. Flip the red one on the left.
100% chance the red one on the right is red.

 

[Fort Fun Indiana]

Ok, if this is a 'riddle' and a play on words, then yup, you got me, I don't see the riddle part

It isn't. "Infinite deck" achieves "with replacement" without reshuffling. Using "with replacement" deems re-shuffling necessary. So it adds unnecessary complexity to the problem.

Do you want to know the correct answers to the 4 scenarios? Or do you have them, now?

 

[Toddsterpatriot]

Restating the riddle in the OP:

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?
.........

2) 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 second card (the one on your right). It is red. What is the probability the other card is red?

...........

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.

What is the probability the card on the left is also red?

In the new scenario,

1) 50%
2) 50%
3) 50%
4) 50%

 

[Fort Fun Indiana]

You didn't replace, reshuffle, or start from scratch in the original.

I tried my best. Sorry.

 

[Fort Fun Indiana]

In the new scenario,

1) 50%
2) 50%
3) 50%
4) 50%

No.

 

[Winco]

It isn't. "Infinite deck" achieves "with replacement" without reshuffling. Using "with replacement" deems re-shuffling necessary. So it adds unnecessary complexity to the problem.

Do you want to know the correct answers to the 4 scenarios? Or do you have them, now?

Sure, let us see what you believe to be the correct answers.

This whole concept of infinity is debateable.
Just like God.
Neither can be proven without changing the definition.

Do you know anything about cardinality? Some infinite sets have more members than other infinite sets.

Like adding 'cardinality' to the definition.

 

[Fort Fun Indiana]

This whole concept of infinity is debateable.
Just like God

Whether infinite numbers or amounts of anything exist is debatable.

Whether "infinite sets" exist in mathematics is not debatable. They do. So do perfect spheres. They and infinte sets are well-defined.

Whether or not we will find objects with these properties in the universe is a separate discussion.

 

[Fort Fun Indiana]

Like adding 'cardinality' to the definition.

Cardinality has no bearing on this riddle, though.

 

[Fort Fun Indiana]

Toddsterpatriot try again?

 

[Fort Fun Indiana]

Winco your answers?

Dogmaphobe ...yours?

 

[Toddsterpatriot]

Toddsterpatriot try again?

I was right, why would I try again?

 

[Fort Fun Indiana]

I was right, why would I try again?

No, unfortunately. You were not correct.

 

[Winco]

We have all given our answers.

I now am ready for what you say is the answer.

 

[Fort Fun Indiana]

We have all given our answers.

I now am ready for what you say is the answer.

1) 1/2

2) 1/2

3) 1/3

4) 1/3

 

[Dogmaphobe]

Dogmaphobe ...yours?

42

 

[Toddsterpatriot]

1) 1/2

2) 1/2

3) 1/3

4) 1/3

You're half right.