Poll: A little math problem
- Thread starter Fud
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Unhappy with theory, I've decided to experiment. I got two $1 coins in change from a nice dish of Kueh Teow. I then proceeded to flip them.
The rules were as follows:
1)Flip both coins at once or in sequence - just so long as nothing else is done until both coins hit the table.
2)Check if at least one is a heads. If not, re-flip without going further.
3)Take out one of the heads coins.
4)What is the other coin? If tails, tally it under your "tails" column (you do have one right?) and if heads, tally under the "heads" column.
5)Repeat steps 1-4 until you get a total of 100 flips (or more if you have the time).
My first tally for this test was 32 heads and 68 tails.
Of course this is not conclusive - perhaps one or both coins were weighted badly. Besides, 100 flips, though not bad, doesn't mean undeniable proof. because of these concerns I will get two new coins and repeat the experiment 100 times with those two. I'll then do the experiment 100 times with another pair of coins and so on. I also encourage anyone who's curious to try the experiment themselves.
The rules were as follows:
1)Flip both coins at once or in sequence - just so long as nothing else is done until both coins hit the table.
2)Check if at least one is a heads. If not, re-flip without going further.
3)Take out one of the heads coins.
4)What is the other coin? If tails, tally it under your "tails" column (you do have one right?) and if heads, tally under the "heads" column.
5)Repeat steps 1-4 until you get a total of 100 flips (or more if you have the time).
My first tally for this test was 32 heads and 68 tails.
Of course this is not conclusive - perhaps one or both coins were weighted badly. Besides, 100 flips, though not bad, doesn't mean undeniable proof. because of these concerns I will get two new coins and repeat the experiment 100 times with those two. I'll then do the experiment 100 times with another pair of coins and so on. I also encourage anyone who's curious to try the experiment themselves.
For some reason, Cheeze doesn't believe that it's okay to reflip. He thinks it is like changing the sex of the dogs or something, and that unless you're getting at least one heads 100 percent of the time, your experiment is obviously flawed.Saskwach post=18.73797.816536 said:
For the last time, Cheeze, this is identical to the situation in the OP's problem. The two dogs have random gender. One happens to be male. This is the same as flipping two coins, where one happens to be heads. If both happen to be tails, it's not the same problem anymore, and can safely be discarded. Effectively, you are narrowing down your case set to correspond to what occurred in the problem.
May I point out that a literal interpretation of this problem leads as follows:Fud post=18.73797.809286 said:
There are two dogs. You're told that both can't be female. This rules out FF.
You are then told to calculate the probability of the 'Other' dog being male. If we think about this completely logically, if both dogs are male, then there is no 'Other' dog. This means that the probability of the 'Other' being male is 0.
Why is my matrix inapplicable? Because we've received new information? But I've modelled that new information perfectly in the matrix. Remember, you agreed that 'you've won one of the bets' could mean different things, you agreed that the proper interpretation was "I've won either bet 1 or bet 2". That leaves you with three equally likely outcomes. How do I know they're equally likely? Because there were four equally likely outcomes to begin with, and we ruled out one.Cheeze_Pavilion post=18.73797.816229 said:
Now you're saying that the information that "I've won either bet 1 or bet 2" entirely invalidates the matrix. Why? Because you know you've won one of the bets? But remember, you've agreed that means "I've won either bet 1 or bet 2", not that you've won a particular bet.
Ok I know you gave up last night on this but this morning I finally found out how to isolate the flaw in your logic.Cheeze_Pavilion post=18.73797.815530 said:
As far as I can tell you would agree with us if the man had stated not that "there is a male" but rather "there are not two females." You believe that these two statements are not the exact same and that the first statement gives you the right to remove one of the M/F F/M choices. The problem with this argument is that these two statements are equivalent.
"there is a male" tells you that there is at least one male and you can infer that there cannot be two females
"there are not two females" tells you that there is not two females and you can infer that there is at least one male.
There is no difference in these two statements.
you are re flipping the coins in this scenario. If it were coins.Cheeze_Pavilion post=18.73797.817437 said:
what I mean by that is you are treating the chance of there being two losses like it was never an option. Your experiment is the exact same as taking one coin placing it as heads and then flipping the other coin and therefore it is 50-50. Even though in our scenarios it did not occur you still have to take into account the chance that it would be two losses not just make that chance a 0%.
You're double-counting "Win Both Bets" here.Cheeze_Pavilion post=18.73797.817437 said:
There is only one set called "Win Both Bets." In "Win Both Bets" is special because it allows either thing to be the referent at the same time.
...
Imagine that we play this "game":
I generate a set that contains at least one male. I then silently pick a "referent," which is any dog that is male.
Then I show you the set and ask "Which of these things was my referent?"
Based on your response, we bin the sets into "Jesse is the referent" and "OSAN is the referent."
Right now what you're doing is putting any set where either of them could be the referent into both bins.
-- Alex
Then how would you separate these two statements. E.G. removing only the FF scenario without removing any other?Cheeze_Pavilion post=18.73797.817449 said:
If you cannot ask yourself again are you inferring something from the statement that is not actually there
this is the part that is not correct. You have put Lose both bet to zero and are re flipping the coins. this is not a continuation of a previous scenario but a whole new one.