Posts by John Doe

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

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?

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

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?

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

John Doe

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?

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

John Doe

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.

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

John Doe

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.

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

John Doe

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.

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

John Doe

The more you have of one gender the better the chances of having more of the same... It increases exponentially...I think...

This is not correct.

For background, I was a math major with an A grade in advanced statistics, so I do know a little about the subject.

Take something with a 1/2 probability of occuring, say a coin toss coming up heads. The probability of tossing a coin three times and having heads come up each time is the probability of getting heads 1 time multiplied by three. i.e., 1/2 x 1/2 x 1/2, or 1/8. To illustrate, let's plot all the possible combinations.

h h h

h h t

h t h

h t t

t h h

t h t

t t h

t t t

That's 8 possible combinations, of which only 1 is all heads. So, our math checks.

This is not the same as saying a man rolls a coin three times, and the first two times are heads. What is the probability of the third roll being heads?

The facts in this scenario have already eliminated all possibilities that do not have heads in the first two rolls. So, taking our rolls from before with bold deleting impossible answers:

h h h

h h t

h t h

h t t

t h h

t h t

t t h

t t t

We see that there are only two possible outcomes left in this scenario. So, the chances of the third roll being heads are 1/2. Make sense?

101

A riddle my brother gave me today

by bohm in

jw
friends

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?.

John Doe

JD - thats not quite right. Try this example: A man has 20 children. He tells you 19 are boys. What is the probability the last one of them is a boy to?

1/2.

101