Question for your Christmas Dinner Guests

[Alan Mendelson]

Here's a question to ask your Christmas Dinner guests while you wait for the turkey:

I am holding a cup with two dice in it. I can see that at least one of the two dice is showing a two. I ask myself "if at least one die in my cup is showing a two what are the odds that the other die is also showing a two?" I immediately reason that there are only six sides on the other die so the answer must be 1 out of 6. I say to my guests am I correct?

Then one of my guests who is a mathematician immediately announces that the correct answer should be 1/11.

But I say I am looking at the dice in the cup and at least one of the two dice is definitely a two, so the answer is 1/6 for the faces on the other die.

The mathematician says he's not looking at the dice so his answer of 1/11 is correct.

But I say I am looking at the dice and I can see one die plain as day.

Now the question for your guests: which answer fits reality?

[quahaug]

We're having prime rib so MERRY CHRISTMAS!!!!

[quahaug]

Oh I forgot. The answer to your question is 1/6. I thought you didn't drink.

[mickeycrimm]

Still looking for a way to try to prove you are right?

[MisterV]

The math guy is pulling your leg.

He can see the contents of the cup.

You innumerates are just too easy ...

[slingshot]

I would ask them, If 2,000 years ago, God gave his only Son to die that we may live, why can't we have Peace on earth, Good Will to men? Merry Christmas, everyone.

[a2a3dseddie]

Here's a question to ask your Christmas Dinner guests while you wait for the turkey:

I am holding a cup with two dice in it. I can see that at least one of the two dice is showing a two. I ask myself "if at least one die in my cup is showing a two what are the odds that the other die is also showing a two?" I immediately reason that there are only six sides on the other die so the answer must be 1 out of 6. I say to my guests am I correct?

Then one of my guests who is a mathematician immediately announces that the correct answer should be 1/11.

But I say I am looking at the dice in the cup and at least one of the two dice is definitely a two, so the answer is 1/6 for the faces on the other die.

The mathematician says he's not looking at the dice so his answer of 1/11 is correct.

But I say I am looking at the dice and I can see one die plain as day.

Now the question for your guests: which answer fits reality?

[RS__]

I'm sure Alan is just a total delight at the Christmas or Thanksgiving table. Sorry, Hanukah*

BTW: Math and science isn't up to popular opinion or majority rule. It's either right or wrong, whether 1% or 99% of people say it's right. In case you don't know what I mean -- it doesn't matter how many people agree with you, you're still wrong.

[Alan Mendelson]

Actually I changed the question around. But no one caught it. Merry Christmas.

[quahaug]

Actually I changed the question around. But no one caught it. Merry Christmas.

Hey, what are you talking about? Everybody "gets it". You wrote a 1/6 answer question.
Drinking again?

[Alan Mendelson]

Never mind. I'm not going to start another 60 page discussion.

[mickeycrimm]

Merry Christmas!

https://www.google.com/url?sa=t&rct=...Wb2RgDSD3BlpDJ

[Dan Druff]

Alan simply can't get past a die having six sides.

[Alan Mendelson]

Actually Dan it's like this: if the guy who looks under the cup and can reason that the answer is 1/6, is it okay for the guy who is given the same information but doesn't look to say the answer is 1/11?

[Dan Druff]

Actually Dan it's like this: if the guy who looks under the cup and can reason that the answer is 1/6, is it okay for the guy who is given the same information but doesn't look to say the answer is 1/11?

Yes, because the odds for figuring out something which already occurred is determined largely by what information you already have.

Take this example:

The Lakers played Minnesota tonight. The game is already over.

If you hadn't followed the game or the score, I could tell you, "The Lakers were at home, but Minnesota is a substantially better team, though not nearly the best team in the league. Neither team played yesterday. What are the chances that the Lakers won?"

You would probably say something like, "40%".

However, let's say that I saw the Lakers were down by 10 with 3 minutes to play, but then turned the game off. If asked what I felt the chances were that they won, I would say, "1%".

Both answers would be reasonable. Why? Because both are answering about an event which already occurred, and both are based upon the amount of information each person had when analyzing the odds of what had happened.

In the question you posed here, if you can see die #1, and it has a 2, then you can eliminate it and the question simply becomes, "What are the chances that there is a 2 on the die you can't see (#2)", which is obviously 1 in 6.

But for the person who can't see die #1, they don't know it's a 2, so that completely changes the odds. They have to figure into the odds what are on BOTH dice. You already have half the results, and they don't.

I hope that explains it.

[Alan Mendelson]

No Dan your answer doesn't explain it because BOTH of the participants know there are only two dice.

The reason you and the others came up with 1/11 is because you ignored that there are two physical dice.

The peeker sees the two dice. The other person is told there are two physical dice but IGNORES the information and instead considers all of the combinations of dice in which there is a 2.

This is a matter of reality vs theory. Using reality the answer is 1/6. The reality is there are only two dice and you can't rotate a die after it comes to rest.

[mickeycrimm]

No Dan your answer doesn't explain it because BOTH of the participants know there are only two dice.

The reason you and the others came up with 1/11 is because you ignored that there are two physical dice.

The peeker sees the two dice. The other person is told there are two physical dice but IGNORES the information and instead considers all of the combinations of dice in which there is a 2.

This is a matter of reality vs theory. Using reality the answer is 1/6. The reality is there are only two dice and you can't rotate a die after it comes to rest.

You are ignoring that you don't know which die the two is on.

[LarryS]

THE WAY ITS WORDED//"at least one of the dice is showng a 2

so it can mean that you are looking at the dice and both have a 2....rendering the answer to be 100 percent.

so there is no answer..it contingent on what you see in front of you. If at least one of the dice has a "2" showing....rather than only one of the dice has a "2" showing

[a2a3dseddie]

THE WAY ITS WORDED//"at least one of the dice is showng a 2

so it can mean that you are looking at the dice and both have a 2....rendering the answer to be 100 percent.

so there is no answer..it contingent on what you see in front of you. If at least one of the dice has a "2" showing....rather than only one of the dice has a "2" showing

You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."
What is the probability that both dice are showing a 2?


There's the original question Larry.

Alan changed the wording in the original question for this thread to get people to agree with his 1/6 answer.

I ask myself "if at least one die in my cup is showing a two what are the odds that the other die is also showing a two?"

[LarryS]

maybe it depends if the other die has a 2 on it or multiple 2s on it. There was no indication that the remaining die was standard. Maybe at least one of the dice is a standard die. Maybe both are. Maybe neither are. Maybe every side of each die has a 2 on it. Maybe the remaining die is an 8 sided die. Maybe they both are 8sided.

https://images.search.yahoo.com/yhs/...g&action=click