3 ms·
Probability as Space
- psyklic 18y agoThe 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 agoTo 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 agoThe 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 agoPeople 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.