I do have to go--windows 7 finally downloaded and I'm going to install it. I'll simply comment that you're now getting into confidence intervals and the notion that as n grows larger, the calculated probability becomes more and more accurate. And I'll once again state that this is a different form of problem. Cheers. Hope to be back later.
A riddle my brother gave me today
John Doe, no, the premise of my statement on page one was there is an uknown probability a given couple will have a boy, and our estimate of that probability may change as we learn more about what children they had. When you write:
No. I did not say that. However, the entire discussion has dealt with a presupposition that we are dealing with things that have equal chances of happening.
Your simply not in line with facts, and must have misread the tired statement i made on page one yet another time. JUST READ IT AND SE WHAT I MEAN.
You also write: "That is statistics "in it's most basic form."" [ie. assigning chance to events which has equal chance of happening]
That may be what you got out of your courses, but in the real world allmost nothing happend with equal chance and you are obviously completely wrong. Symmetry arguments play a big part in actual statistics, but you DONT want to come up with such a limited definition.
I think you have demonstrated that you dont have anything but a hand-waving definition of what a probability is, aside that it is equal at events which are equally likely. Whoop-de-whoop. You have also shown you are unable to apply that definition to anything but the most trivial problems, namely coin tosses and the like.
Yet even though you are unable to give a proper definition, you insist i am wrong for some unspecified reason. I assume its because it does not fit your pre-conceived notion of what a probability is, even though its not clear to yourself.
count me unimpressed.
Your reply to my challenge was:
I'll simply comment that you're now getting into confidence intervals and the notion that as n grows larger, the calculated probability becomes more and more accurate. And I'll once again state that this is a different form of problem. Cheers. Hope to be back later.
Well, what is the probability? are you saying you are unable to give an answer, or that no answer exist?
No, those are two different cases because the order matters. The case of first-born son, second born daughter isn't the same as first-born daughter, second-born son.
After sleeping on it, I see that the "Tuesday" is an important clue the informed observer gave us, and I didn't consider it. You who said 13/27 are right! The observer excluded all but 27 possibilities:
- Seven with a first-born son born on Tuesday and a second-born daughter born on any day
- Seven with a first-born daughter born on any day and a second-born son born on Tuesday
- Six with a first-born son born on Tuesday and a second-born son not born on Tuesday
- Six with a first-born son not born on Tuesday and a second-born son born on Tuesday
- One with a first-born son and second-born son, both born on Tuesday (don't count this case twice!)
So 13 of the 27 possibilities are two sons. My hat is off to those who saw this the first time!
GLT - the very first class the very first day at university, i was having a class in combinatorics. The teacher walk in, a big man with a funny haircut in worn out slippers, look around and said: "This course is nothing but being able to count. Thats what i have to teach you, and its very hard because you think its so easy you dont take it serious".
I salute you and Ann for being good counters!
Sorry I didn't give you credit where it was due. I didn't have time to go back and see who had said 13/27 before getting to work this morning. That odd figure stood out, I just had to figure out where it came from and if it was right or wrong. As usual, you were right!
Thank you for the fun thread! I didn't read your response until this evening.
Solving this class of problem requires more than one tool. The first tool is the basic probability part, identifying the number of permuations (there are 196: (two genders x seven days of the week) ^ two children = 14 ^ 2 = 196). The second tool is deductive reasoning, determining which of the permutations the observer's statements have excluded. You need to use both tools to make sense of "Monty Hall Problems": it isn't just about finding the over-all distribution, it's identifying which particular outcomes are consistent with observations based on "inside knowledge" of the permutation that turned up in this particular instance. It looks like a pure probability problem, but the reporter with inside information changes the game.
John, let me help you. What is the probability the next flight to new york will fall down over the atlantic? There are two outcomes as i see it: It fall down, or it does not. So how do i go from those to the probability? I assume you dont want to tell me its 1/2.
That reminds me of the classic video at http://www.thedailyshow.com/watch/thu-april-30-2009/large-hadron-collider that there was a 50:50 chance the hadron collider would destroy the world with a black hole. You have to love the US education system.
Regarding the original riddle - A man has 2 children. He tells you one is a boy born on a tuesday. What is the probability the other is a boy to?- it was an english riddle, not a maths one. It would have been easier to spot if you had included a comma.
A man has 2 children. He tells you one is a boy, born on a tuesday. What is the probability the other is a boy too?
It does show how easy it is to misunderstand each other, and why the JWs often have different understandings over their own beliefs, depending on what part of a sentence or article they feel carries the most weight.
I do have to go--windows 7 finally downloaded and I'm going to install it. Cheers. Hope to be back later.
John Doe - if you buy a Mac for college you can get a free iPod Touch!
That could solve your PC issues and your Maths, English and humility issues all in one go. Result!
GLT - its a good illustration of what is going on. At first we know nothing (aside the outcome space), ie. our belief is smeared out over all 196 states. Then, as we get more information, our lack of belief decrease, ie. the number of avaliable states; first through the information one is a boy, secondly through the information that boy was born on a tuesday; we could actually calculate this information gain exactly by finding the entropy as this:
Originally we have 2 bits of information in our system (ie it can be specified by 2 bits)
After we gain the first piece of information (one is a boy), the total amount of bits of uncertainty is 1.59 bits. (log(3))
Then, after we gain the second piece of information, our uncertainty regarding one of the states (2 boys) goes UP, but the total uncertainty regarding the overall system goes down to 1.52 (a = 13/27, b = (1-a)/2, entropy: -2*b*log(b) - a*log(a)).
Its quite easy to explain what happends with our uncertainty this way and put numbers on it, but what about the other way, ie. we are told one is born on a tuesday, then the one born on a tuesday is a boy? Then we would begin with 2 bits of uncertainty to, and we end up the same place, but meanwhile the value of the two pieces of information change.
jwfacts - that movie is excellent! you just cant make up people like Dr. Ellis, noticed his office?
Its scary that wagner guy gets to teach science, but John Olliver got him pretty good near the end. If he is not a lying crook, i do wonder why he dont play the lottery - perhaps he has a strange notions that only things which has never been tried before has a 50-50 chance of happening?
Im completely unable to tell the difference between between the sentence with and without the comma - i guess thats a big part of the problem! :-).
JD - You have told me several times i dont understand what a probability is, but so far you have been completely and utterly unable to demonstrate a) where i am wrong, b) that you know enough of the subject to give your own definition which apply to anything else than fair coin tosses (your reply to this seem to indicate that you think statistics is all about fair coin tosses), c) solve the simplest of dataanalysis problems. Your reply to these things has been very evasive.
I want to have a fact-based discussion. If you want your input to be taken seriously on subjects where you are not an expert, ie. global warming, i think its all but fair to call you out on a very easy subject for you to discuss, one where you claim to have some expert knowledge, and one where you are very willing to tell other people they are wrong.
btt for john doe.