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LobowolfXXX
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I have two dice, one red and the other green. I propose to roll them both behind a screen, where you can't see them, and that when at least one of them comes up "6," I'll reveal a 6. I begin to roll the dice, and after a few tries, I stop and show you the red die, which is, in fact, a 6. What are the odds that the green die is also a 6?
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
magicjohn2278
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About 1 in 6 (Roughly!)...?
Steve Martin
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I am supposed to be getting some work done this week, Wolf...

:)
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein
stanalger
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I think we'd have to know what rule you'd use to decide which
die to show us if BOTH dice landed with sixes on top.

Here are three rules and the corresponding answers.

"Always show the red if both are sixes,"
Answer: 1/6.

"Always show the green if both are sixes."
Answer: 0

"If both are sixes, flip a coin. If H, show the red. If T, show the green."
Answer: 1/11

Other rules could give other answers.

Stan Alger
LobowolfXXX
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Quote:
On 2006-03-09 14:45, stanalger wrote:
I think we'd have to know what rule you'd use to decide which
die to show us if BOTH dice landed with sixes on top.

Here are three rules and the corresponding answers.

"Always show the red if both are sixes,"
Answer: 1/6.

"Always show the green if both are sixes."
Answer: 0

"If both are sixes, flip a coin. If H, show the red. If T, show the green."
Answer: 1/11

Other rules could give other answers.

Stan Alger



Fair enough...if both are sixes, the choice as to which to show will be random. Your coin flip works well enough.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
magicjohn2278
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Quote:
On 2006-03-09 14:45, stanalger wrote:
I think we'd have to know what rule you'd use to decide which
die to show us if BOTH dice landed with sixes on top.

Here are two rules and the corresponding answers.

"Always show the red if both are sixes,"
Answer: 1/6.

"Flip a coin. If H, show the red. If T, show the green."
Answer: 1/11

Other rules could give other answers.

Stan Alger




Why use a coin, why not use the dice again? Smile
stanalger
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Quote:
On 2006-03-09 14:49, LobowolfXXX wrote:

Fair enough...if both are sixes, the choice as to which to show will be random. Your coin flip works well enough.


Then I'll stick with 1/11.

Stan
Steve Martin
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Yes, I agree.

1/11

0.090909
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein
magicjohn2278
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I DON'T GET IT!!!

The chances of rolling two sixes are 1 in 36, but if one dice IS a 6 then the chances of the other dice being a six must be 1 in 6? - No? (I don't care which dice you show me!)
Steve Martin
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Well, John, to simplify it, consider this:

My friend has two dogs. He brought them to me for the first time, each in a totally opaque plastic box. We placed both boxes in a "male-dog-detectometer" that revealed to me that at least one of the dogs was in fact male. What is the probability that the other dog is male too?
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein
LobowolfXXX
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Ahhh, the spirit of harmony. Yes, the a priori odds are that 1 time in 11, if there is at least one six, there will be double sixes, to wit (red die first):
6-1
6-2
6-3
6-4
6-5
6-6
1-6
2-6
3-6
4-6
5-6

Now, back in the old days, one might have said, "But, wolf!! Once the red die is shown to be a six, the last five possibilities can be eliminated!!

This objection is, of course...TRUE.

BUT those five outcomes can be multiplied by 1 (the chance that, if they existed, the red die is the one you'd see), whereas the 6-6 outcome has to be multiplied by 1/2 (the chance that, if it existed, the red die is the one you'd see).

Saints be praised, that makes it 5 to 1/2 against, or for those of you who hate fractions, 10-1, or for those of you who love fractions... 1/11 -- perfectly consistent with the initial odds. God bless us every one!
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
stanalger
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"If both show sixes, roll the red again.
If it shows 1 or 2, show the red (with the 6 back on top).
If it shows 3, 4, 5, or 6, show the green."

Answer: 1/16

(Forget the screen for this one. Imagine the procedure is carried out
and the results are emailed to someone else. All they get is
"Red" or "Green" and the details of the experiment--including the rule
for dealing with double sixes.)
TomasB
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There are only six possible cases to consider and I'll write the relative probabilities since you divide with their total probability later.

Six cases where you show Red

R666666
G123456

You might at first think that the relative probability of all those six cases is the same, but remember that throwing 66 you only show the Red half of those times. So the relative probabilities for the six cases are

R666666
G123456
P11111˝

To get the conditional probability you take the desired case and divide with the accumulated relative probabilities of all the valid cases:

˝/(1+1+1+1+1+˝)=1/11

/Tomas
magicjohn2278
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Quote:
On 2006-03-09 15:00, stanalger wrote:
"If both show sixes, roll the red again.
If it shows 1 or 2, show the red (with the 6 back on top).
If it shows 3, 4, 5, or 6, show the green."



Shouldn't that be "If both show sixes, roll the green again.
If it shows 1 or 2 or 3, 4, or 5 show the red.
If it shows 6, show the green.

.. NOW it makes sense!
TomasB
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And Stan is of course right with the result if you throw the Red die again. Just substitute 1/3 for 1/2 in what I just wrote.

/Tomas
magicjohn2278
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Quote:
On 2006-03-09 15:02, TomasB wrote:

Six cases where you show Red

R666666
G123456

/Tomas


What happened to the six cases where you show Green?

G666666
R123456
TomasB
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And in John's case it'd be 5/6 / (1+1+1+1+1+5/6) = 5/7

/Tomas
TomasB
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Quote:
On 2006-03-09 15:07, magicjohn2278 wrote:
Quote:
On 2006-03-09 15:02, TomasB wrote:

Six cases where you show Red

R666666
G123456

/Tomas


What happened to the six cases where you show Green?

G666666
R123456


Red is shown...not Green. Had five of those cases occurred he'd have been forced to show Green, but he didn't, hence their probability is zero.

/Tomas
stanalger
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Give me a number between 0 and 1 inclusive,
and I'll give you a rule which, when implemented,
makes your number the answer to the original question.

(Don't expect a quick response. I'm leaving my computer now.
Don't know when I'll get back to the Café.)

Stan
magicjohn2278
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Quote:
On 2006-03-09 15:10, TomasB wrote:
Red is shown...not Green. Had five of those cases occurred he'd have been forced to show Green, but he didn't, hence their probability is zero.

/Tomas


Ahh but!!!! That is based on the exact wording of the question! If he had thrown 6-6, and randomly chosen whether to show us red or green, if he had chosen the green, then we could say with 100% probability that the green dice was a 6.

So what are the odds now?
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