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Hm... I'm not sure you're answering the correct question. Assume you're a man and you have a sister. Your next sibling is about to be born. There is a 50% cha

by tomp 10y ago

Hm... I'm not sure you're answering the correct question. Assume you're a man and you have a sister. Your next sibling is about to be born. There is a 50% chance that it's a boy! In which case, he will have one brother (you), you will have one brother (him), and your sister will have 2 brothers. She wins. There is a 50% chance that it's a girl! In which case, both she and your other sister will both have 1 brother (you), whereas you won't have any. You loose again!

ewjordan 10y ago
"Assume you're a man and you have a sister." You just put your finger on the scale. All you can assume is that you're a man, not that you have a sister.
- wernercd 10y ago
  4 siblings... 2 boys, 2 girls... 50/50... The girls each have 2 brothers... The boys each have 1 brother. 6 siblings, 3/3... 8 siblings, 4/4... etc
  - tempestn 10y ago
    The problem is that you're not considering all the other cases. Here are the possibilities with 2 siblings: Gender: B,B B,G G,B G,G # brothers: 1,1 0,1 1,0 0,0 Average # of brothers for boys: 0.5 Average # of brothers for girls: 0.5 You can see that in the families with a mix of boys and girls, the girls do indeed have more brothers. But this is balanced out by the families with more (or in this case all) of one or the other.
  - pklausler 10y ago
    Sure. Limit families to four children. There's one way to have zero daughters. In BBBB, each of the four boys has 3 brothers. Score 12 for the boys here. There's four ways to have one daughter. In each of them, she's got 3 brothers, while the 3 boys each have 2 brothers. Score 12 for the girls, 24 for the boys. There's six ways to have two daughters. In each of them, the 2 girls each have 2 brothers, while the 2 boys each have 1 brother. Score 24 for the girls, 12 for the boys. There's four ways to have three daughters. In each of them, the 3 girls each have one brother, and the boy has none. Score 12 for the girls, zero for the boys. There's one way to have four daughters, but obviously nobody has a brother. Add up the scores, and you'll see a tie at 48. (EDIT: Bogus expected value removed after re-reading.)

by tomp 10y ago

ewjordan 10y ago

"Assume you're a man and you have a sister." You just put your finger on the scale. All you can assume is that you're a man, not that you have a sister.

wernercd 10y ago
4 siblings... 2 boys, 2 girls... 50/50... The girls each have 2 brothers... The boys each have 1 brother. 6 siblings, 3/3... 8 siblings, 4/4... etc
- tempestn 10y ago
  The problem is that you're not considering all the other cases. Here are the possibilities with 2 siblings: Gender: B,B B,G G,B G,G # brothers: 1,1 0,1 1,0 0,0 Average # of brothers for boys: 0.5 Average # of brothers for girls: 0.5 You can see that in the families with a mix of boys and girls, the girls do indeed have more brothers. But this is balanced out by the families with more (or in this case all) of one or the other.
- pklausler 10y ago
  Sure. Limit families to four children. There's one way to have zero daughters. In BBBB, each of the four boys has 3 brothers. Score 12 for the boys here. There's four ways to have one daughter. In each of them, she's got 3 brothers, while the 3 boys each have 2 brothers. Score 12 for the girls, 24 for the boys. There's six ways to have two daughters. In each of them, the 2 girls each have 2 brothers, while the 2 boys each have 1 brother. Score 24 for the girls, 12 for the boys. There's four ways to have three daughters. In each of them, the 3 girls each have one brother, and the boy has none. Score 12 for the girls, zero for the boys. There's one way to have four daughters, but obviously nobody has a brother. Add up the scores, and you'll see a tie at 48. (EDIT: Bogus expected value removed after re-reading.)