A simple logic problem

[Kruser6]

Here ya go Illini. This will save you some typing for these people that just don't get it.


WHAT IS THE PROBALITY OF A MOTHER HAVING A GIRL AFTER HAVING THREE BOYS IN A ROW.?
OR WHAT IS THE PROBABILTIY OF HAVING FOUR BOYS AFTER HAVING THREE BOYS IN A ROW.

The answer is quite simply for both cases: 50%

We can assume that the chances to have a boy or a girl are the same,
50%. Then GIVEN the fact that the family has three boys in a row, the
event "sex of new baby" is completely independent from the event "sex
of previous babies".
The problem is similar to toss a coin and, after getting three tails
you wonder which is the probability to get a head in the next toss.
Because each toss is independent from the other (the coin still have
two sides), the probability is 50%.

For further reading and references see the following pages:
"Chapter 6 - PROBABILITY ":
"However, one part of the traditional material is useful and easily
mastered. It concerns successful repetitions of an event. Suppose
there is a 50% chance of having a girl baby and a 50% chance of having
a boy. The question is: What happens to the 50% as we specify longer
and longer strings of girls born to the same mother? Some students
have had enough instruction in probability to remember something about
chances remaining the same. Partial memories will lead them astray if
they believe that the chances of two girls (and no boys) in a family
of 2 children are the same as the chances of one girl in a family of
one child. There is something that remains the same and it is just
that initial 50%. We get the probability of an event happening ?in a
row? by using the base probability, the 50%. But whatever we do, we
clearly must arrive at smaller chances for more difficult or more
unlikely events. It is harder to get two girls in a row, with no
intervention from boys, than to get a single girl at the beginning.
It is harder to get five heads in a row with a coin than to get one
head with one flip.
If half the babies born are girls, and all those with daughters have a
second child and the chances of a girl are always 50%, then half of
those with a girl the first time will have a girl the second time.
Half had a girl the first time and half of that half will have a girl
the second time. ... "

</pre>

 

[Illini]

No - that's not what the problem asks anyway. You've already formed one half of your pair of children. You did not have a girl first, so you cannot be part of the families that had 2 girls (GG). Your pair of children will either be BG or BB - and while you cannot be part of the GB group, a stranger cannot know that if the only information he's provided with is that one of your children is a boy. You'll be the only one knowing that you had a boy first. Hence, for the person answering the problem, there's 2 chances out of 3 that your other child is a girl (BG or GB, out of BG, GB and BB).

The problem asks what is the probability of the second child being a girl. The solution is that it's the same probability as if it were the first born child. The fact that this family is not going to be a GG family doesn't mean anything.

 

[fhmesq44]

Illini,

Excluding the case of two girls, what is the probability that two random children are of different gender?

That is the same question asked in a different way.

 

[Kruser6]

No. We are talking about the sex of the second child.

You know nothing about that second child, only that it was born. Anything you know about the first child is completely and totally irrelevant as to the sex of the second child.

Let me change this for you.


"We are talking about the 2nd spin on a roulette table"

You know nothing about that next spin, only that it will land on a number" Anything that you know about the last spin is completely and totally irrelevent as to the end result of the 2nd spin.

If people can hopefully relate this to a roulette table maybe they won't continue to try and argue this.

 

[Doug]

100%

"He starts talking about his SON" implying the other is a daughter. If this has been said already forgive me, I didn't want to read 6 pages.

Doug <script type="text/javascript"> vbmenu_register("postmenu_6275539", true); </script>
More Trees,Less BUSH !



Join Date: Nov 2002
Location: None are enslaved more than those who falsely believe they are free !
Posts: 24,966


<!-- icon and title -->

<hr style="color: rgb(253, 222, 130); background-color: rgb(253, 222, 130);" size="1"> <!-- / icon and title --> <!-- message --> A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?

........................................................................................................

I'll change my answer to 100%

It's a trick question.

The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.

 

[festeringZit]

We are not talking about statistics and averages. We are talking about a random event.....having a second child.

Every time you have a child, it's 50% girl, 50% boy.

Illini,

We're not talking about looking at one child, and then evaluating
the probability on the birth of the second.

We are talking about finding out about an existing set of two kids,
ruling out the case where they are both girls, and then making statements
about that scenario.

 

[Kruser6]

Doug <script type="text/javascript"> vbmenu_register("postmenu_6275539", true); </script>
More Trees,Less BUSH !



Join Date: Nov 2002
Location: None are enslaved more than those who falsely believe they are free !
Posts: 24,966


<!-- icon and title -->

<hr style="color: rgb(253, 222, 130); background-color: rgb(253, 222, 130);" size="1"> <!-- / icon and title --> <!-- message --> A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?

........................................................................................................

I'll change my answer to 100%

It's a trick question.

The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.

We think alike! It was the first thing I thought of when I read this.

 

[JaBrady]

haven't read all the thread but if the original question said what is the chance the other child is a boy what would the answer be?

1/3?

BB
BG
GB
GG

 

[festeringZit]

Ok. Screw it, I'm back to taking bets on this. I will bet any amount
on this problem that the answer is 2/3.

Bring it on.

 

[Kruser6]

The logic on 2/3 using the BB, BG, GB, and GG method is also retarded.

For what reason would you have a BG and a GB.

The set of kids can be a BB or a BG. So basically 1/2 and 50%. You can't count BG and GB as 2 sets as they are the same thing regardless of the order you put them in.

 

[Illini]

Illini,

We're not talking about looking at one child, and then evaluating
the probability on the birth of the second.

We are talking about finding out about an existing set of two kids,
ruling out the case where they are both girls, and then making statements
about that scenario.

Well, the "sets" thing is not logical thinking. Logic says you draw conclusions about what you know.

If a=b and b=c, then a=c. Nothing about the first child correlates with the second child in any way. The probability remains random at 50%.

It's Logic 101.

 

[Geoff101]

Zit...pm me...Im making arrangements to come down in two weeks...let's put the locig to the test, then you can report back who made money...no ill will...im fun to drink with....

 

[Illini]

Ok. Screw it, I'm back to taking bets on this. I will bet any amount
on this problem that the answer is 2/3.

Bring it on.

All you can eat here.

 

[Illini]

We think alike! It was the first thing I thought of when I read this.

That's just a distraction. Maybe the guy calls his one son "shortstop" and his non-athlete son he just calls his son.

 

[CoolBreeze22]

which NBA team does the guy with 1400 kids play for???

 

[fhmesq44]

Well, the "sets" thing is not logical thinking. Logic says you draw conclusions about what you know.

If a=b and b=c, then a=c. Nothing about the first child correlates with the second child in any way. The probability remains random at 50%.

It's Logic 101.

exactly and what you know is that there is a boy, you don't know if he is older or younger, so you know B, but you don't know if it is BG, GB or BB. I'm posting a damn poll.

 

[festeringZit]

haven't read all the thread but if the original question said what is the chance the other child is a boy what would the answer be?

1/3?

BB
BG
GB
GG

Yes 1/3.

Givena family w/ two kids that has at least one boy, the probability they
are both boys is 1/3.

 

[Illini]

Illini,

Excluding the case of two girls, what is the probability that two random children are of different gender?

That is the same question asked in a different way.

The fact that he has one son doesn't exclude anything. That's where you are drawing conclusions that aren't really there.

So what if he isnt going to have two girls. So what. Means nothing.

 

[Illini]

exactly and what you know is that there is a boy, you don't know if he is older or younger, so you know B, but you don't know if it is BG, GB or BB. I'm posting a damn poll.

The poll won't mean anything because most people are stupid.

Not calling you stupid, but you are drawing conclusions here that don't exist.

 

[Kruser6]

Illini since nobody will explain there logic to me can you please explain why they are counting GB and BG as two pairs when they really are just the same?

There are two possibilities here. BG and BB. 1/2 is a girl so 50%!!!!