Somebody (think it was PawnCurry) stated correctly that additional
information might change probabilities. But does it matter HOW one
gets this information???
Assume A knows that the guard wouldn't tell him anything about
himself. But, anyhow, A is more interested in B's fate than in his own (may be, B is A's son). So A asks the guard "will B live?" and the guard says "NO, B will die"
What do we have now?
Originally posted by EdSchwartzIt doesn't matter HOW you get the information, but the case is that you are trying to compare DIFFERENT information. You can't look at the answer without looking at the question.
Somebody (think it was PawnCurry) stated correctly that additional
information might change probabilities. But does it matter HOW one
gets this information???
Assume A knows that the guard wouldn't tell him anything about
himself. But, anyhow, A is more interested in B's fate than in his own (may be, B is A's son). So A asks the guard "will B live?" and the guard says "NO, B will die"
What do we have now?
In the original problem the 1st information is not simply "B will die" but "From the other 2 prisioners, at least B will die".
Subtle difference but it's enough to ammount to different probabilities.
In your new question, after the guard's answer, A and C would have a 50% chance of survival each. Remember that C could not be named as well.
Probability in itself means nothing. Now follow me here: If you had a BAG with all the real numbers in it what is the chance that if you pull out a number it will be a natural one? The probability of this event occuring is 0. And yet it is, as any sound person can see, a possible outcome.
Interesting...
Originally posted by PawnCurryI was thinking along these lines, and was going to set some parameters for one of the computer gurus to make a math model, and let it play out for say, a million or so tries. Then compile the results, and accept the outcome. No time at the moment though, when I get a chance to log back on.🙂
Trust me, not wrong!!!
I've tried my hardest to explain so can only blame myself for not explaining it clearly enough. It is a tough one to get your head round... but the only way to do it is to ditch your usual assumptions, look at the possibilities, and do the maths.
Or you could try your own experiment with a friend, three cups to represent the c ...[text shortened]... r hunt on the net for the Monty Hall problem. And then tell me if you'd switch boxes or not...!
Originally posted by Palynka
In the original problem the 1st information is not simply "B will die" but "From the other 2 prisioners, at least B will die".
OK now, the guard shows up in A's cell: "Hey Mr.A, here are the
latest news: From the other guys at least B will die". Even assumed
that A knows the guard would not tell him anything about himself,
there are two possible outcomes: B&A will die OR B&C will die ....
Originally posted by EdSchwartzBut the fact there are two outcomes doesn't mean that they are equally probable. Buy a lottery ticket and there will be two outcomes: you win or you lose. Are the odds 50%? Obviously not.
OK now, the guard shows up in A's cell: "Hey Mr.A, here are the
latest news: From the other guys at least B will die". Even assumed
that A knows the guard would not tell him anything about himself,
there are two possible outcomes: B&A will die OR B&C will die ....
By your new problem it is not clear, even in the spirit of the problem, if the guard had a 50% chance of saying B dies in the case B&C die. If yes, then A's chances are still 1/3.
Originally posted by Polynikesyour right i just wish i would have said it first. too much deep thinking going on here. if i tried deep thinking my head would heat up so fast my hair would catch fire 😳
It seems to me that his chances do not increase from 1/3 to 1/2.
Reason being, there is a 100% chance that B or C will be named. His question,
“tell me the name of one person (B or C) who is to be executed.”
tells him absolutely nothing at all. Of course, at least one of them is to die. The guard's answer only tells us what we already know. ...[text shortened]... im, and no math or reasoning can possibly increase your odds of survival. Now lights out.
Their chances are equal. Here is why.
They each start with a 1/3 survival chance...nobody argues that fact.
Multiply this times 1 million random scenarios and you will get something dangerously close to:
A survives 333,333 times
B survives 333,333 times
C survives 333,333 times
Good so far, right?
OK, now entering the equation with that knowledge, as A does, you learn that B doesn't survive. That's all that you learn, B doesn't survive. Even if C hears the conversation he knows the same thing, B doesn't survive.
So you eliminate all of our random scenarios where B survived and you are left with 666,666 randomly genereated scenarios where A or C survive. What are their respective totals? 333,333 each.
Translation, their respective chance for surviving out of the three is still the same: 1/3. BUT, their survival probability relative to each other is 50/50. The limitation on the guard's answer is what is confusing you.
Wrong. From the guard's answer you learn that from the subgroup {B,C} at least B dies.
Your calculations are all wrong. If you're going to use the 1.000.000 random cases argument you have to consider which answers the guard would give.
Using your logic (and strange calculations):
333.333 times A survives: 166.666 times the guard says B, 166.666 times the guard says C
333.333 times B survives: 333.333 times the guard says C
333.333 times C survives 333.333 times the guard says B
When the guard says B he eliminates 500.000 possibilities and 500.000 remain
166.666 when A survives and 333.333 when C survives. 1/3 for A, 2/3 for C.
Palynka, the problem with factoring in the guard's answer as being specific to C's chances is that the guard is not allowed to consider A's chances. Therefore, anything he says relative to C is invalidated. All we learn from the guard is that B dies. Nothing else can be garnered from his statement.
Originally posted by PalynkaNot the case. Either I am seeing this more clearly than the rest of the thread participants...or I am a complete dolt. The overwhelming majority would support the latter. 😀
For some time now I have the feeling you are just having some laughs and seeing how far will we go.