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"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.
by 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 ago4 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 agoThe 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 agoSure. 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.)