On: Nobody Understands Probability

[thwarted]

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox has interesting content in the sections Second Question and Ambiguous Problem Statements.

I'll accept that I'm wrong and that the answer is 1/3 and that I just don't understand it and that I'm supporting the point that "no one understands probability, especially me", but there has been little explanation why the birth order is even a factor. Even that Wikipedia entry labels the four possibilities with "older child" and "younger child", which seems to be extra, unneeded information when the term "at least" is used to describe the number of boys independent of order.

[abeppu → thwarted]

Birth order per se doesn't matter; probability mass does. Birth order is an easy way to show that you're twice as likely to get a boy and a girl as you are to get two boys. But you can ignore birth order and say instead "let k be a binomially distributed random variable with n=2 and p=1/2. If you know k>=1 what is p(k=2)?". Then the answer is a straight comparison of p(k=2) to p(k=1), where we note that '2 choose 1' is 2, and '2 choose 2' is 1. Note that ordering per se isn't entering into this, but to someone without probability background, it's a bit obtuse. Describing the probability space in terms of birth order is not strictly necessary but helps a lot of people grasp the concept.

[iliketosleep → thwarted]

i think it's like this.... interpretation 1.. we select a random FAMILY from the set of all families with two children.one of the children happens to be a boy. {BB, BG, GB} are possibilities. P(BB) = 1/3

interpretation 2.. we select a random CHILD from the set of all families with two children. one of the children happens to be a boy. in this case we have the following possible combinations [B1B2, G1B3, B4G2]. we know it's a boy, so what's the probability that B1 or B2 was selected? 1/4+1/4 = 1/2.