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LobowolfXXX Inner circle La Famiglia 1196 Posts 
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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." |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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About 1 in 6 (Roughly!)...?
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Steve Martin Inner circle 1119 Posts
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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 |
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stanalger Special user St. Louis, MO 998 Posts
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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 |
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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Quote:
On 2006-03-09 14:45, stanalger wrote: 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." |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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Quote:
On 2006-03-09 14:45, stanalger wrote: Why use a coin, why not use the dice again? 
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stanalger Special user St. Louis, MO 998 Posts
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Quote:
On 2006-03-09 14:49, LobowolfXXX wrote: Then I'll stick with 1/11. Stan |
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Steve Martin Inner circle 1119 Posts
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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 |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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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!) |
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Steve Martin Inner circle 1119 Posts
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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 |
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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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." |
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stanalger Special user St. Louis, MO 998 Posts
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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.) |
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TomasB Inner circle Sweden 1144 Posts
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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 P11111½ To get the conditional probability you take the desired case and divide with the accumulated relative probabilities of all the valid cases: ½/(1+1+1+1+1+½)=1/11 /Tomas |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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Quote:
On 2006-03-09 15:00, stanalger wrote: 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! |
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TomasB Inner circle Sweden 1144 Posts
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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 |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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Quote:
On 2006-03-09 15:02, TomasB wrote: What happened to the six cases where you show Green? G666666 R123456 |
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TomasB Inner circle Sweden 1144 Posts
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And in John's case it'd be 5/6 / (1+1+1+1+1+5/6) = 5/7
/Tomas |
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TomasB Inner circle Sweden 1144 Posts
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Quote:
On 2006-03-09 15:07, magicjohn2278 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 |
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stanalger Special user St. Louis, MO 998 Posts
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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 |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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Quote:
On 2006-03-09 15:10, TomasB wrote: 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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Posted: Mar 9, 2006 07:35 pm 
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