I remember way early in the thread you mentioned that you favored a 1/6 interpretation.
At the time your comment made me think to myself that I favored the 1/11 interpretation because I think it is the more interesting scenario and analysis.
But I’ve come around to thinking that at least one type of 1/6 scenario requires the least amount of assumptions.
Which is why I would have thought you’d consider yourself in the “not enough info to give a single answer” camp.
Doesn’t really matter much I guess - the comment I responded to made it sound like there were lots of people in a “1/6 and 1/6 only” camp and that didn’t fit my perception so I questioned it.
The post of yours I was responding to started with you saying:
*I would argue that the only reasonable interpretation of the boy-girl problem is the one which yields 1/2. *
It’s “The boy-girl problem.” It’s a specific question asked specific way, and it doesn’t have only one reasonable interpretation you claim it does, especially for the reason you claim that is so. Understanding how to solve these problems have real-world applications; it’s irrelevant that the specific situations within the problems themselves will probably never arise within one’s lifetime.
Okay, in that case. But the phrasing of the boy-girl problem has a different case than a completely different case you think it should be.
As a reminder, this thread started with “A math teacher friend of mine shared this problem…”
No! Rolling both at the same time and rolling them sequentially are very different.
The OP is more like roll both dice until at least one of them is a 6, what are the chances that the other is also a 6? It takes fewer rolls on average to get 1+ 6 out of two dice than a 6 out of 1 dice.
How so? Before you furnish your answer, you may wish to reflect on the fact that it’s physically impossible to throw two dice at *exactly *the same time.
It says “You are ten”, it doesn’t say that the die shows a ten.
But its 1 out of 6. It doesn’t matter what was on the other die, it’s 1 out of 6. If you are rolling a six-sided die, and there’s a six on exactly one face of that die, then it is 1 out of 6. That is, unless someone played a dirty trick on you and replaced the 6 with a different number.
You may as well ask what the chances are of rolling a 6 on a die if you are in the 6th row of the number 6 bus going down 6th avenue, you are six minutes late for work on the 6th floor of room 666, and its 6/6/66. They are all independent of one another.
This question is presented in a confusing manner, but is very easy, if one properly understands sample spaces.
When 2 six sided dice, 1 Green and 1 Red, are rolled, and you want to consider only those outcomes that include either die showing a 6, there are only 11 possible results:
My deep attitude is the “not enough info to give a single answer” camp.
My negotiating tactic in the thread has been to consistently give examples in the 1/6 camp while explaining that that’s a choice, not a foregone conclusion. And an arguable choice at that. I picked the minority approach hoping to coax the majority folks off their “It’s gotta be 1/11 there’s no other possibility!” bandwagon.
Once they can admit there are two possibilities, then it’s time to stick the wedge in the crack and pound away until we get awareness of the full panoply of choices. Of admittedly varying plausibility.
One of the resident professional math experts (**Chronos ** I believe) has laid this full line of reasoning out several times. And been mostly on ignore by everyone else. To my ongoing amazement.
Why can’t he? It would be empirical confirmation of the analytical answer of 1/11.
I don’t know why folks are making the question out to be some form of semantic gotcha. What’s so puzzling about a pair of fair dice were rolled and one person was shown a 6?
What details are sufficient to satisfy everyone who may claim the question is ambiguous? Can you write it in such a way that no one could claim ambiguity?
This is adding information not stated in the problem. At no point does it say that they picked one die at random and read the number. The number 6 is given in the problem without any means for it to be different, and thus is fixed. Any simulation must keep the 6, or else it is modeling a different problem. And once you do require there to be a 6, the 1/11 interpretation is the only one that works.
I do not understand why such an explanation is still being promoted, when one of the basic rules of word problems is that all required information is given.
How can you show a 6 if one isn’t rolled? Again, making the assumption that people are being honest, etc.
And supposedly the OP’s question is modeled after a different question in which a 4 is shown. In which case there is a correct answer, 2/11, as a choice.
You asked what details were necessary to satisfy everyone about ambiguity so I gave my input.
I want it explicitly stated that he is throwing out 25/36 of the rolls by only asking about a pre-determined number.
Why wouldn’t you state that explicitly if it is the case? It doesn’t hurt anything to state it that way does it? Why frame the question in a way that can leave people in doubt about the rules of the game?
Because showing a 6 or a 2 or a 4 is enough to know that that particular number was in fact shown. It’s a given.
If I say I have 3 black socks, 1 gray sock, and 1 paisley sock in my sock drawer and I draw one black one completely randomly what does anything else matter if the question then asks what’s the probability that the next sock randomly drawn is gray? At some point normal assumptions should be sufficient.
I’m just trying to imagine getting through an engineering curriculum with this standard of precision required.