Two coin puzzle

Quote: 1call2many

To calculate the second probability I can ask which coin was chosen? Is it White with white or White with Black (only two coins in bag) so 1/2 is my answer.

The 2/3 answer implies that there are 2/3 ways to draw the white/white coin and only 1/3 ways to draw the white/black coin from a bag?

This is an awesome thread!

The problem is you don't know which coin was chosen---
You could be looking at side 1 of the white/white coin. = other side is white
You could be looking at side 2 of the white/white coin. = other side is white
You could be looking at side 1 of the white/black coin. = other side is black

2 out of 3 will be white.

It took me a little to fully grasp this concept. Thanks to all for explaining their thoughts. Kudos on doing the experiment Icall2many.

Posters are answering two questions on this thread: the one asked and one that is pretty close but not the one asked.


The question asked:

You randomly draw one coin and observe one side only which is white. What is the probabilty that the other side of that coin is white? [My emphasis.]




The question many posters thnk was asked but was not:

If you randomly draw a coin and observe one side only as white, what is the probability the other side will be white?

I don't know how to use spoiler tags. There are two coins. Most people are saying there is a 2/3 chance that they drew one of two random coins? That makes no sense. You are all wrong. If you choose a random coin, and it is always the white side face up, there is a 50% the other side is white or black, based on the problem. There's a 100% chance the white side will be facing you, not 3/4.

1/1 (given) x 1/2 (two coins) = 50%

3/4 (white sides) x 2/3 (white sides) = 6/12 = 50% chances you would see two white sides chosen randomly

There is never a 2/3 chance of anything.

Quote: Sonuvabish

There is never a 2/3 chance of anything.

I present logic to the contrary in my post above, under the question not asked that many thought was.

Quote: BleedingChipsSlowly

I present logic to the contrary in my post above, under the question not asked that many thought was.

I read it, but I don't agree. If you are saying you pull both coins out and look only at one, which is always white, then randomly guess which one of three sides is white, then there is a 2/3 chance you are right. Regardless, your thinking is obviously superior to most of the forum!

Quote: JoePloppy

This is an awesome thread!

The problem is you don't know which coin was chosen---
You could be looking at side 1 of the white/white coin. = other side is white
You could be looking at side 2 of the white/white coin. = other side is white
You could be looking at side 1 of the white/black coin. = other side is black

Show Spoiler

I'm a bigot

Dude, you think there is a greater than 67% chance you chose a random coin out of 2 possible coins? If I have an all white quarter, and a quarter painted white only on heads, and i randomly choose 1, what are the chances I will flip two black tails in a row?

Quote: Sonuvabish

Quote: JoePloppy

This is an awesome thread!

The problem is you don't know which coin was chosen---
You could be looking at side 1 of the white/white coin. = other side is white
You could be looking at side 2 of the white/white coin. = other side is white
You could be looking at side 1 of the white/black coin. = other side is black

Show Spoiler

I'm a bigot

Dude, you think there is a greater than 67% chance you chose a random coin out of 2 possible coins? If I have an all white quarter, and a quarter painted white only on heads, and i randomly choose 1, what are the chances I will flip two black tails in a row?

I think you need to reread the question, dude. And for the record, 2/3 is LESS than 67%

2/3

Quote: Sonuvabish

I read it, but I don't agree.

Perfencly fine, I'm not always right. Thank you for taking the time to read what I wrote.

Quote: Sonuvabish

Regardless, your thinking is obviously superior to most of the forum!

I am smart enough to know that that is not true. Several forum members could kick my ass, logically speaking, standing on one foot with one hand tied behind their back. If it's any solice I had to think long and hard about this problem. Actually, the basic logic was presented in another thread I posted to involving the probabilty that a second child would be a boy. Anyway, having spent some time teaching I do think I have a knack for presenting problems in a way that fosters insight.

Ok, big boy, let's you and me have it out. At the bar. No pythons, no pit bulls. Smoke if you would like. $100 buyin to make it interesting. We use a sack with two coins, one white on both sides, the other black on one side and white on the other. For each round you wager $3 and I wager $5. An impartial chimp draws one of the coins and slaps it down on the table. If the upside is black it's a push. If the upside is white the flip side decides the winner. If the flip side is white I win your $3. I f the flip side is black you get my $5. Are you in?

It's 1/2. How is this controversial?

Quote: RS

It's 1/2. How is this controversial?

No controversy, I'm just a kind old soul that wants to give away my money.