You can keep your $100
http://en.wikipedia.org/wiki/Boy_or_Girl
The Boy or Girl problem is a well-known example in probability theory:
Second question
Neither order nor age is important. There are four possible child combinations for a two-child family as seen in the sample space above. Three of these families meet the criteria of having at least one boy. The set of possibilities (possible combinations of children that meet the given criteria) is:
<table class="wikitable"> <tbody><tr> <th>Older child</th> <th>Younger child</th> </tr> <tr> <td><s>Girl</s></td> <td><s>Girl</s></td> </tr> <tr> <td>Girl</td> <td>Boy</td> </tr> <tr> <td>Boy</td> <td>Girl</td> </tr> <tr> <td>Boy</td> <td>Boy</td> </tr> </tbody></table>
[edit] Bayesian approach
Consider the sample space of 2-child families.
Therefore the probability is 2/3.
http://en.wikipedia.org/wiki/Boy_or_Girl
The Boy or Girl problem is a well-known example in probability theory:
- A random two-child family whose older child is a boy is chosen. What is the probability that the younger child is a girl? (Or: choose a random two-child family assuring that the older one is a boy. What is the probability that the other one is a girl?)
- A random two-child family with at least one boy is chosen. What is the probability that it has a girl? (Or: choose a random two-child family assuring that at least one is a boy. What is the probability that the other one is a girl?)
- in the first case, there are two equally probable possibilities: the second one is a boy or a girl.
- in the second case, there are three equally probable ways in which at least one child can be a boy: only the older one, only the younger one, or both.
Second question
- A random two-child family with at least one boy is chosen. What is the probability that it has a girl?
Neither order nor age is important. There are four possible child combinations for a two-child family as seen in the sample space above. Three of these families meet the criteria of having at least one boy. The set of possibilities (possible combinations of children that meet the given criteria) is:
<table class="wikitable"> <tbody><tr> <th>Older child</th> <th>Younger child</th> </tr> <tr> <td><s>Girl</s></td> <td><s>Girl</s></td> </tr> <tr> <td>Girl</td> <td>Boy</td> </tr> <tr> <td>Boy</td> <td>Girl</td> </tr> <tr> <td>Boy</td> <td>Boy</td> </tr> </tbody></table>
[edit] Bayesian approach
Consider the sample space of 2-child families.
- Let X be the event that the family has one boy and one girl.
- Let Y be the event that the family has at least one boy.
- Then:
-
Therefore the probability is 2/3.
hno:I'm done with you, you're either a total idiot, or you are trolling
just to be annoying.
Here is the original question:
"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? "
It seems a review of combinations vs. permutations is in order...
See: http://www.mathsisfun.com/combinatorics/combinations-permutations.html
If order does not matter (which it doesn't in this case) and you have two equal possibilities, then the chance of either of those possibilities being valid is 50%. The other child can be only a boy or a girl, THAT'S IT. They are both as likely to be true.
The line "He does not tell you whether the son is the oldest child or the youngest child." has no influence on the question.
See: http://www.mathsisfun.com/combinatorics/combinations-permutations.html
If order does not matter (which it doesn't in this case) and you have two equal possibilities, then the chance of either of those possibilities being valid is 50%. The other child can be only a boy or a girl, THAT'S IT. They are both as likely to be true.
The line "He does not tell you whether the son is the oldest child or the youngest child." has no influence on the question.
I'm not actually good at math - so I'd take what I've typed with a grain of salt, it just makes the most sense to me that the gender of the first child is irrelevent to the question - and thus you have a simple set, either {B} or {G}. I can't see how there is a difference between the question the father asks and the question "I have one child, what is the probability it's a girl?"
But like I said, grain of salt.
Zit, you arent equating it correctly...it is worded differently than your wikipedia...that's where you're going wrong...
with 2 coins, kids, deer, whatever...you flip the first one, it is heads....what are the odds on the second one being heads?
or you have a frying pan and a plate....you flipped the plate already and it landed upside right, what are the odds the frying pan lands upside right when you flip it?
50%
with 2 coins, kids, deer, whatever...you flip the first one, it is heads....what are the odds on the second one being heads?
or you have a frying pan and a plate....you flipped the plate already and it landed upside right, what are the odds the frying pan lands upside right when you flip it?
50%
