3 ms·

The real point of confusion is that people don't realize that BG/GB are two separate states. Like many of the recent blog articles, this one also doesn't clearl

by psyklic 18y ago

The real point of confusion is that people don't realize that BG/GB are two separate states. Like many of the recent blog articles, this one also doesn't clearly explain why you need to consider both BG and GB. Consider: "A person has two kids, and his first-born is a boy. What is the probability the other is a boy?" There are two possibilities, each equally likely -- (first-born, second-born): (B,B) and (B,G). Hence, 1/2. "A person has two kids, and one is a boy. What is the probability the other is a boy?" In other words: "The first-born is a boy AND/OR the second-born is a boy." There are three possibilities, each equally likely -- (first-born, second-born): (B,B), (B,G), and (G,B). Hence, 1/3.

psyklic 18y ago
To be more clear: When hearing this problem, some people imagine -- (one-kid, other-kid): (B,G) and (B,B), hence 1/2. Others imagine -- (first-born, second-born): (B,B), (B,G), (G,B), hence 1/3. Someone needs to write a blog post explaining why the latter method is superior, not just a blog post that automatically enumerates the four states. People need a REASON for not combining BG/GB, and considering the children as (first-born, second-born) provides much of that reason, since it is a logical way of ordering children. A (one-child, other-child) ordering appears a bit absurd, even to the layperson.
- jballanc 18y ago
  The reason is that the two children are different dimensions in the probability space. Both (one-kid, other-kid), and (first-born, second-born) yield the same space, and both will give a 1/3 answer.
  - psyklic 18y ago
    People interpret "one kid is a boy" as "first-born is a boy" in my example above (i.e. they selectively choose which kid is the "one kid" -- the one which is a boy), which yields 1/2. People seem to be good at enumerating the "probability space" quite well. They just don't understand why the dimensions are what they are.

by psyklic 18y ago

psyklic 18y ago

To be more clear: When hearing this problem, some people imagine -- (one-kid, other-kid): (B,G) and (B,B), hence 1/2. Others imagine -- (first-born, second-born): (B,B), (B,G), (G,B), hence 1/3. Someone needs to write a blog post explaining why the latter method is superior, not just a blog post that automatically enumerates the four states. People need a REASON for not combining BG/GB, and considering the children as (first-born, second-born) provides much of that reason, since it is a logical way of ordering children. A (one-child, other-child) ordering appears a bit absurd, even to the layperson.

jballanc 18y ago
The reason is that the two children are different dimensions in the probability space. Both (one-kid, other-kid), and (first-born, second-born) yield the same space, and both will give a 1/3 answer.
- psyklic 18y ago
  People interpret "one kid is a boy" as "first-born is a boy" in my example above (i.e. they selectively choose which kid is the "one kid" -- the one which is a boy), which yields 1/2. People seem to be good at enumerating the "probability space" quite well. They just don't understand why the dimensions are what they are.