|
|
|
|||
| Go to page [Previous] 1~2~3~4~5~6~7~8 [Next] | ||||||||||
magicjohn2278 Special user Isle of Man UK 544 Posts 
|
..on a slightly more sensible note, I STILL think there is an argument for saying that a man who owns two dogs, and one is male, has a 50/50 that his other dog is a male.
As we KNOW that one dog is male, why toss a coin twice? We only want to establish the sex of the other dog.... |
|||||||||
Steve Martin Inner circle 1119 Posts
|
Lobowolf... can you correct the slip in your question, and I'll try to give an answer to it? Thanks.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
LobowolfXXX Inner circle La Famiglia 1196 Posts
|
I meant to say: In each case, what are the odds that the penny is heads?
"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." |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
In each case, before you make the flips, the possible results are:
Nickel:H, Penny:H Nickel:T, Penny:H Nickel:H, Penny:T Nickel:T, Penny:T In each case, you are specifying (in the question) that the Nickel happened to turn up heads, and you show me the Nickel. Your showing me the Nickel in each case does not change the fact that in each case the probability that the Penny turned up heads is 1/2. This is the same as my argument in "coin game 2". Does this get us anywhere we havn't been already, or have I missed something (I may have done)?
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
Thanks to Lobowolf, I have completely changed my view on this puzzle now.
I now agree with him that the correct answer to the puzzle as stated is 1/2. Here is an attempt at a simple explanation, based on all our discussions: There are four possible scenarios: Dog 1: M, Dog 2: M Dog 1: M, Dog 2: F Dog 1: F, Dog 2: M Dog 1: F, Dog 2: F When someone (who knows both dogs) tells you that one of the dogs is male, the fact is that although YOU don't know which one he is talking about, HE DOES. Therefore, when he makes the statement "one of the dogs is male" he is actually identifying a *specific* dog, whether YOU know it or not (which you don't). Therefore, not only does that statement eliminate the FF pairing, it actually DOES also eliminate the opposite MF pairing to the one that applies to this particular pair of dogs. (This is different to what I argued before, as I previously believed that both MF and FM pairings should remain under consideration by you.) Therefore, there are only two scenarios for you to consider: Dog: M, Dog: M Dog: M, Dog: F So it is equally likely that the other dog is male as female. (This is exactly like "coin game 2" in which the result of a specific coin is given). This is a big U-turn... I only hope that my reasoning is not foolish!
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
magicjohn2278 Special user Isle of Man UK 544 Posts
|
Quote:
On 2006-03-09 11:07, Steve Martin wrote: I quite agree with you, but can't help thinking that someone is going to argue that if the dogs are identical, then he WON'T know which one he is talking about......? |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
I have a niggling doubt about my reasoning. This puzzle has completely trashed my week!
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
magicjohn2278 Special user Isle of Man UK 544 Posts
|
.. I just hope that I never meet Sergey Smirnov.... he has a lot to answer for!
|
|||||||||
|
LobowolfXXX Inner circle La Famiglia 1196 Posts
|
Quote:
On 2006-03-09 09:58, Steve Martin wrote: Steve - I submit to you that in one of the three cases I outlined, the odds that the penny is heads is 1/3, while in the other two cases, the odds, as you stated, are 50-50. I'm off to run an errand, but I'll check the board in about 2 hours and explain further. I don't want to say which case I'm talking about, so I'll let you mull it over.
"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." |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
I think, therefore, that there is another error in the wording of your question:
"In each case, I flip both coins behind a screen, then show you a nickel. It is heads." Maybe you meant to say: "In each case, I flip both coins behind a screen, then show you a COIN (if allowed to do so by my own stated rule). If I show you a coin, it is heads." I answered the first version and I stick by my answer 
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
stanalger Special user St. Louis, MO 998 Posts
|
Quote:
On 2006-03-04 21:59, LobowolfXXX wrote: Exactly. Here is Sergey's original wording: "Your new friend has two dogs. You know the sex of one of them - it is male. What is the probability that the other one is also male?" How did you obtain the information that one of them is male? As stated, the problem is ambiguous. It depends on how you know one of the dogs is male. Stan |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
Lobowolf,
To follow up my previous post: Given my corrected wording to the question... it is in scenario 2) that the odds that the Penny is heads are 2/3.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
magicjohn2278 Special user Isle of Man UK 544 Posts
|
Quote:
How did you obtain the information that one of them is male? No it doesn't, once we know one is male it's simply a question of guessing the sex of the other. I wonder what the options are? |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
Lobowolf,
Correction... (ignore my previous post) Given my corrected wording to the question... it is in scenario 2) - given that you have shown me a nickel with heads - that the odds that the penny is also heads is 1/3. This nicely demonstrates that the framing of the question is important.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
|
LobowolfXXX Inner circle La Famiglia 1196 Posts
|
Quote:
On 2006-03-09 11:45, Steve Martin wrote: Steve - This time, for once, I actually meant what I said...in all three situations, I show you a nickel. In all three situations, it's heads. But in one of the situations, the odds on the penny's being heads are 1 in 3, not 50-50. I'll tell you why in about 1/2 hour.
"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." |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
Yes - sorry, my brain is fried. Ignore those recent corrections I tried to make.
In scenario 2), you show me a nickel that is heads. The probability that the penny is also heads is 1/3. This is because, having told me that heads on one of coins is the criteria, then H-H, H-T and T-H are all up for consideration. This is equivalent to the dog puzzle where we say beforehand that if one of the dogs is male, I will tell you. This gives us the 1/3 - 2/3 split. If we don't say that ahead of time, but just choose one of the dogs's sex to reveal at random, we have the 1/2 - 1/2 split.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
TomasB Inner circle Sweden 1144 Posts
|
I see the ambiguity too...I think. If the pair happens to be mixed we _could_ assume that he choses the gender to name randomly with a square distribution. If such a person says that one dog is male we should strike one of the MF FM in the table as it is just 0.5 probability that he would say Male on either one of them. Or rather multiply each of their probabilities with 0.5, which gives the same result.
The only way the 2/3 answer would be true is if we _know_ that this person would name Male when the pair is mixed. Good call, Wolf. So how can we reformulate the question to specify either case? The first scenario is easy I think. "After seeing one of the dogs he says that at least one is male." That'd happen in 50% of the cases where the pair is mixed and in 100% of the cases where there is MM. But how can it be formulated to force the second scenario? Wonders, /Tomas |
|||||||||
|
TomasB Inner circle Sweden 1144 Posts
|
I have a weird way to force the second one:
You have an allergy to Male dogs. There are two dogs in the room that you can't visually tell the gender of. You start to sneeze, so you know that one of them is Male. What is the probability that the other is Female? /Tomas PS Again, good call, Wolf. |
|||||||||
|
LobowolfXXX Inner circle La Famiglia 1196 Posts
|
Quote:
On 2006-03-09 12:46, TomasB wrote: Oooh, that's good!! (the sneezing thing, I mean) Yes, I think I could have simplified this long ago, but unfortunately, each time, I wrote AS I thought, rather than after I thought. You nailed it...it seems there are two independent events to multiply - the flip of the first coin and the flip of the second coin; there is actually a third event - the choice of which coin to show; in some cases, that choice will be automatic, and in other cases, it will be constrained.
"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." |
|||||||||
|
Steve Martin Inner circle 1119 Posts
|
Tomas - very nice on the allergy
"After seeing one of the dogs he says that at least one is male." Are you formulating that phrase (instead of "after seeing both dogs he says that at least one is male") to avoid the issue of having to assume a square distribution for his random choice of call? If so, I understand. Fun thread
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
|||||||||
| The Magic Cafe Forum Index » » Puzzle me this... » » What are the odds? (0 Likes) | ||||||||||
| Go to page [Previous] 1~2~3~4~5~6~7~8 [Next] | ||||||||||
Posted: Mar 9, 2006 02:18 pm 
| [ Top of Page ] |
|
All content & postings Copyright © 2001-2024 Steve Brooks. All Rights Reserved. This page was created in 0.03 seconds requiring 5 database queries. |
|
The views and comments expressed on The Magic Café are not necessarily those of The Magic Café, Steve Brooks, or Steve Brooks Magic. > Privacy Statement < 
|