# A riddle my brother gave me today

by bohm 101 Replies latest jw friends

• ##### John Doe
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?

• ##### John Doe
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?

• ##### GLTirebiter

There's a subtle trick to the question. It doesn't say whether the first or second child is a boy, only that at least one of them is. This bias in the reporting changes the result from the expected 50/50 probability: by revealing at least one is a boy, the probability of the second being a boy is no longer a statistically independent occurrance.

Consider: there are four equally possible sequences for the gender of two children

Boy, Boy

Boy, Girl

Girl, Boy

Girl, Girl <-- this is the only case that is excluded

So of the three remaining cases, only one is the case of two boys: the probability is 1/3.

This is a relative of the Monty Hall Problem. What looks like a random selection really isn't, because the use of inside information biases the reporting: if there were two girls, he would have switched the riddle around.

• ##### today

So what's the answer? For real.

• ##### recovering

1 Boy, Boy

2 Boy, Girl

3 Girl, Boy

4 Girl, Girl <-- this is the only case that is excluded

there is a problem with your logic gl , 2 and 3 are equal solutions hence 1 there are only two possible solutions, this makes it a 50 % chance of it being 2 boys

• ##### bohm

GLTirebiter: You would be completely right were it not for the information about the day of the week.

Recovering: No, 1, 2, 3, 4 are all equally likely a-priori, ie. happend with probability 1/4. the extra information, ie. one is a boy, excludes number 4, which mean 1, 2, 3 are equally likely.
But you, to, are not using the information about the day of the week which change the picture.

today: The actual solution was first posted by StAnn, later i posted a short calculation.

StAnn: it still crack me up i had two math majors stamp in the ground and insist on 1/2 while you stubbornly actually worked out the problem and got the result. i would never had such luck if i tumbled into your subject!

John Doe: There is a couple of problems here. You wrote:

"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?"

First off, i have NOT been hostile to changeling. I started this thread as a kind of joke. Changeling wrote something about the problem which, if interpreted litterally, using the mathematical definition of the words probability, chance, etc., is not correct. However, i think the gist of what changeling wrote is correct and for that reason i reformulated what she wrote slightly such that it WAS correct and said "yes you are right". TELL ME HOW THAT IS BEING BLATANTLY HOSTILE TO ANYONE WHO DISAGREE WITH ME?

Now you come in and you, with your math training, see that changelings statement is wrong if one interpret it completely litteral. So you come down on Changeling like a ton of bricks and on me to for saying changeling is correct, even though it should be darn clear from the context (and the fact i wrote it a gazillion times) i only stood by what i wrote, if it should be taken litterally. YOU are the one picking nits here.

I then made a very carefull explanation for you what was going on, and you began quotinging me out of context. what i wrote was this:

Changelings statement is wrong when you read it litterally for a lot of reasons. I believe this is because Changeling is not used to expressing herself in mathematical terms, and use her intuitive interpretation of the words "probability", "chance", etc. I choose not to jump up like a smug smartass geek and cry: "Your wrong!!!" because i see no point in that.
...

Notice my statement is different from Changeling, but i think changeling is trying to say what i wrote
...

So let me be abselutely clear (but uncivil to changeling): I defend the statements i have formulated, not changelings, because they are obviously wrong since she lived a life instead of taking math courses

It should be pretty clear that when i write "obviously wrong" i mean that she misuse certain terms that people who have wasted their time taking math courses understand in a different manner, but i think the gist of what she wrote is correct. Changeling is wrong in the sence i am wrong when i misspell stuff and place the wrong commas, or i use the wrong words when discussing american politics. I believe it has no bearing of the value of what she write, or her intelligence. The last part - that she lived a life instead of taking math courses - was a joke, Gettit?

• ##### bohm

John Doe:

Your telling me i dont know what a probability is, and you strut your math-major and statistics courses. Well count me unimpressed, i think you are only good for anything when you can point the spotlight onto people without professional training and tell them they are wrong.

lets try to review what you have written regarding probabilities and put that math-major and statistics courses to the test. You gave the following definition:

A probability is nothing more than the ratio of an occurence to non occurence. This is determined solely by the enumeration of possible outcomes

Later you clarified this:

Possible" outcomes are not "actual" outcomes. Do I need to elaborate further?

Yes i think you should because its not a workable definition! So lets say you are told that a given couple has had 3 children, all of which are boys, and you are asked what the probability is the next is a boy to. What "outcomes" will you enumerate, how does these correspond to the occurances and non-occurances and what ratio will you calculate?

Try to explain it to me in all details. This is not connected to the riddle, so none of my assumptions are valid anymore. A person who has any training in statistics should be able to formulate an imprecise problem and work on it from there.

• ##### John Doe
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?

• ##### bohm

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 ...

And - i want to add - if you want to use "occurance" or "nonoccurance" in the defintion, SPECIFY what they mean with respect to your enumeration.

"The reason both I and another person with math training missed the problem is worth noting."

Yes indeed.

Any other bits of wisdom such as what a "waste" of time math classes are?

its a joke, i even wrote that earlier. damn..

UPDATED.

• ##### John Doe
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.