4 ms·

(F,M,1) means met daughter (who is older) first. (M, F, 2) is met son who is younger than his sister first. These is the space of possible ways to meet his two

by Dn_Ab 16y ago

(F,M,1) means met daughter (who is older) first. (M, F, 2) is met son who is younger than his sister first. These is the space of possible ways to meet his two kids ordered by age.

Tichy 16y ago
I see - I thought the first child you meet is always a boy in your example. So I am still not sure what you are calculating, but at least I understand the tuple notation :-)
- Dn_Ab 16y ago
  I was trying to make a point that two problems that look the same actually lead to different results based on what information you are given. For example, being told someone has 2 kids and at least one is a girl then the space for this is S = {(M,F), (F,M), (F,F)}. However if I were to run into someone with two kids and saw a daughter then the information I have doesn't allow me to construct the space S above if I wanted to find the chance of say, 2 girls while accounting for age. Instead I must consider S X {1,2} because instead of knowing that there is at least one daughter I just know that I have met one daughter whose age (whether older) is unknown to me. I know nothing of her sibling. So I am calculating the possible ways I could have met her and then the chance of 2 daughters conditioned on that space. This is a very tricky differentiation. Distinctions like this and thinking about what to condition on is what makes probability so tricky.
  - Tichy 16y ago
    I must admit, I don't understand the distinction. What does age have to do with it? The information seems to be the same in both cases: a man with two kids, at least one of them a girl. Of course thinking about age is a legit way to calculate the probability of the second kid being a girl. It is just unnecessarily complicated.
    - Dn_Ab 16y ago
      The distinction is in how the information was presented and there is a difference (let us ignore the ages and assume i met the younger one then seeing as I met one girl my space is {(F,F), (F,M)} vs {(F,F), (F,M), (M,F)} for at least one girl while accounting for age). For the second age does not matter so much as who is older and accounting for all combinations is why I present it that way. The distinction is tricky but problems like these are often covered in the conditional probabilities section of most probability theory texts.

by Dn_Ab 16y ago

(F,M,1) means met daughter (who is older) first. (M, F, 2) is met son who is younger than his sister first. These is the space of possible ways to meet his two kids ordered by age.

Tichy 16y ago

I see - I thought the first child you meet is always a boy in your example. So I am still not sure what you are calculating, but at least I understand the tuple notation :-)

Dn_Ab 16y ago
I was trying to make a point that two problems that look the same actually lead to different results based on what information you are given. For example, being told someone has 2 kids and at least one is a girl then the space for this is S = {(M,F), (F,M), (F,F)}. However if I were to run into someone with two kids and saw a daughter then the information I have doesn't allow me to construct the space S above if I wanted to find the chance of say, 2 girls while accounting for age. Instead I must consider S X {1,2} because instead of knowing that there is at least one daughter I just know that I have met one daughter whose age (whether older) is unknown to me. I know nothing of her sibling. So I am calculating the possible ways I could have met her and then the chance of 2 daughters conditioned on that space. This is a very tricky differentiation. Distinctions like this and thinking about what to condition on is what makes probability so tricky.
- Tichy 16y ago
  I must admit, I don't understand the distinction. What does age have to do with it? The information seems to be the same in both cases: a man with two kids, at least one of them a girl. Of course thinking about age is a legit way to calculate the probability of the second kid being a girl. It is just unnecessarily complicated.
  - Dn_Ab 16y ago
    The distinction is in how the information was presented and there is a difference (let us ignore the ages and assume i met the younger one then seeing as I met one girl my space is {(F,F), (F,M)} vs {(F,F), (F,M), (M,F)} for at least one girl while accounting for age). For the second age does not matter so much as who is older and accounting for all combinations is why I present it that way. The distinction is tricky but problems like these are often covered in the conditional probabilities section of most probability theory texts.