Cheeze_Pavilion post=18.73797.815471 said:
What beginning are you talking about? The beginning of the *question* or the beginning of the *experiment*? Of course I would manipulate my experiment at the start and call it realistic--as long as I was manipulating my experiment to model the reality as described by the question, the WHOLE question, not just the beginning of the question. So help me Monty Hall.
So, say you have two coins, Coin 1, and Coin 2. Just like this problem, when you ask if one of them is heads, the answer is "yes." So you lay down Coin 1 as heads. Then, in the problem, you ask if one is tails, and the answer is "yes" so you lay down Coin 2 as tails. This is how you would approach this problem, correct? Yes, based on what you've said so far.
So, what are the odds that Coin 1 is heads? 100 percent? Really? No. The odds are 50 percent. Because in the solution set:
MM MF FM FF, you have ruled out option MM, and option FF, but it could be either MF or FM.
Umm, the probability of any event that is actually known to have occurred is 1. Solution sets are for figuring out the probability of events that are not yet known either because they have not yet occurred or we do not have full knowledge of them. So yes--if you lay Coin 1 down Heads up, the probability that it is Heads 100%
If that changes later on in the problem, you're equivocated along the way about one of the terms you used, which is where your mistake is.
All right, first, your experiment isn't random.
But relating to your comment on my proposed problem. I wasn't saying that laying down coins is the way you're actually supposed to do this. I'm saying this is the way you would do it, based on your response to the original problem. Essentially, you say that if you know one is heads, you lay down Coin 1 as heads. So if they then say that one is tails, you've got to lay down Coin 2 as tails. This is the way you're thinking about the original problem.
But what are the chances that Coin 1 is heads? Not 100 percent, as it is in this problem. Coin 2 could be heads, and Coin 1 could be tails, and the premise of the problem would still be satisfied. But the way you're going about it, the results are incorrect here, with the chances for each coin being absolutely determined.
So where we differ in our logic relates to how we set up the problem. You would like for the washer woman to say "yes" 100 percent of the time. But don't you see that this is not realistic. There is a certain chance that she would say "yes" and a certain chance that she would say "no," if you actually did this experiment. Manipulating it so she definitely says "yes" leads you to an answer which is, ultimately, incorrect. Are you saying that the washer woman made sure there was a male dog before the question was asked? That's what this amounts to.
The fact that she *happens* to say yes doesn't mean she says yes 100 percent of the time. It only means that in this case, there *happened* to be at least 1 male dog. This is why it's a random experiment. Assuring that she will always say yes invalidates the whole question. The point is that these are 2 random dogs, and that either or both of them could be female or male, and that this case just happened to fall within the 75 percent where there was at least one dog.
I'm not sure if you are deliberately misunderstanding this, or what. You've seen proof, you've had relatively solid explananations. But I've tried to explain problems like this before (such as Monty Hall) to people who didn't believe the answer, and I know how difficult it can be. But I mean, even the OP said the answer was 33 percent, from where he got the problem, and more than half of people still think that the answer is 50 percent.
