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?.
I am allmost certain you have completed the statistics courses, and you are correcting me and slapping me over the head but you are completely and utterly wrong.
Did you not read where I conceded that I was incorrect in my initial analysis? What do you want, a pint of blood? Has there been any disagreement as to what a probability is? I get the strong impression that you are simply yanking my chain, and frankly, I grow weary of it.
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?.
A person who has any training in statistics should be able to formulate an imprecise problem and work on it from there.
Were you or were you not asking for an example? I've given a rigorous and thorough defintion of probability.
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?.
JD, wrote:
Statistics and probability, it its most basic form, is simply a ratio formulated from all possible outcomes in a given scenario. Keeping it simple, take a coin toss. One coin toss. The possible outcomes are heads and tails. (ignoring the minute chance it may land on its side) Therefore, the "probability" of any one side coming up in a single toss is the ratio of that outcome to the possible outcomes. Back to our coin toss, it's either heads or tails. Heads is one possibility. Tails is another possibility. The two, distinct possibilities, when added together, gives a total of two, to be redundant. The probability of heads occuring in one coin toss, for example, is 1 (the number of possible occurences that heads comes up) / 2 (the enumeration of the total possible occurances). Even though we are only dealing with 1 occurnce, there are 2 possible occurences.
Okay, you are not giving a definition, you are giving an example, a very long and convoluted one that is. I conclude you have still not been able to give a proper definition of what a probability is, nor give an answer to the extremely simple problem i gave you in the last post. So let me ask you again, after one has enumerated the possible outcomes of a given situation (for example, boy/girl, head/tail, side1, 2, 3, 4, 5, 6 of a dice), what does one do then? Complete the sentence: The probability of an event is ...
Sigh.
You have no desire to discuss the problem, do you.
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?.
Yes i think you should because its not a workable definition!
Statistics and probability, it its most basic form, is simply a ratio formulated from all possible outcomes in a given scenario. Keeping it simple, take a coin toss. One coin toss. The possible outcomes are heads and tails. (ignoring the minute chance it may land on its side) Therefore, the "probability" of any one side coming up in a single toss is the ratio of that outcome to the possible outcomes. Back to our coin toss, it's either heads or tails. Heads is one possibility. Tails is another possibility. The two, distinct possibilities, when added together, gives a total of two, to be redundant. The probability of heads occuring in one coin toss, for example, is 1 (the number of possible occurences that heads comes up) / 2 (the enumeration of the total possible occurances). Even though we are only dealing with 1 occurnce, there are 2 possible occurences.
Have I beat the dead horse long enough?
Changeling wrote something about the problem which, if interpreted litterally, using the mathematical definition of the words probability, chance, etc., is not correct.
I in no way support materially changing what someone has said and saying it is correct. If you want to ask if she meant "x or z," then go ahead. I still do not think your reading of her meaning is correct.
The reason both I and another person with math training missed the problem is worth noting. A common error the average person makes is assuming that having a series of consecutive and uniform outcomes affects the chance of obtaining the same outcome on another roll, and is a point has been made quite often. Identifying the problem as being of this type is an easy thing to do, and it's a short step to shutting down further analyzation. Ironically, it boils down to semantics--something you claim to dislike.
Furthermore, I think you misread me. I offer my background, not as "parading" it around, but simply to state that I do have significant knowledge in this regard. I welcome being proved wrong, and it does not bother me. I offer my knowledge to any who care to benefit/use it. When I say something is "incorrect," I'm stating a simple fact, not "coming down on someone like a ton of bricks." Once I say something is incorrect, I promptly offer an explanation of the reasons, especially when prompted. People who do not offer prompt explanations when questioned annoy me to no end, such as you have done with this thread.
Any other bits of wisdom such as what a "waste" of time math classes are?
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?.
because they are obviously wrong since she lived a life instead of taking math courses.
Why the blatant hostility to everyone disagreeing with you in this thread? You talk about civility, yet you make statements like this. Have I warranted them?
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?.
Bohm, not only am I NOT a math major: I'm an ART major.
StAnn
You're not going to cut your ear off and give it to a prostitute are you?
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?.
a couple of things here. First off, when talking about the probability the next child will be a boy, what are the occurances and non-occurances exactly you use to calculate that ratio?. Secondly, it would seem we have at most one occurance, namely one future birth.
At any rate this seem to come down to belief a given event will occur, which is then again based on our subjective knowledge.
i will be happy to hear you elaborate on this without copy-pasting :-).
If I copy paste, I divulge the fact when doing so. You can be certain I did not use google in my posts--had I done so, I would not have been mistaken.
I should have been more clear. Pay attention to the last sentence you quoted:
This is determined solely by the enumeration of possible outcomes.
"Possible" outcomes are not "actual" outcomes. Do I need to elaborate further?
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?.
Ok, I'm back. Worked overtime last night and didn't get home until 3 am.
First of all, I want to acknowledge that I was incorrect. I made a simple assumption that was not supported by the puzzle; namely, that the first child was the boy. The information I gave regarding coin toss statistics is correct, but I did not apply it correctly to this problem. When you automatically assume which child is a boy, it eliminates potential outcomes, as has been pointed out.
"
A probability is nothing more than the ratio of an occurence to non occurence. This is determined solely by the enumeration of possible outcomes. A particular occurance in a specific chance has no bearing on the probability of the next occurance. Therefore, the statement that the more boys you have the higher the chance the next one will be a boy is patently and conclusively false."
Now lets review my actual statement:
Why? Your actual statement was not under consideration. I was solely speaking about changeling's statement and your saying that her statement was only incorrect under some conditions. Hence "the statement." Or, are you saying I misread changeling?
Side note for changeling: You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.
In the problem, we neglect this effect and assume a=1/2 for both births. Ie. i ask the problem under the most simple assumptions.
So its pretty damn clear i never wrote the probability the next will be a boy will be higher, i wrote our belief the next will be a boy will increase. That you begin your post by writing that: "You stated the assumption was that the probability of having a boy is 1/2. " is a red herring, since i clearly indicated that i was NOT discussing the riddle with my post by my last statement which i have underlined.
"Belief" has nothing to do with the problem as worded--it is strictly one of statistics. Probability is probability.
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?.
JD - changeling is only wrong if one assume that no couples has more likelihood to have boys than girls. I am not a biologist, but i believe that is wrong.
You stated the assumption was that the probability of having a boy is 1/2.
we assume a-priori there is a 1/2 chance to give birth to a boy independent of past births, no twins, and no more boys or babies are born on tuesdays than other days of the week
A probability is nothing more than the ratio of a possible occurence to a possible non occurence. This is determined solely by the enumeration of possible outcomes. A particular occurance in a specific chance has no bearing on the probability of the next occurance. Therefore, the statement that the more boys you have the higher the chance the next one will be a boy is patently and conclusively false.
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?.
Side note for changeling: You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.
That is not correct.
