Families Keep Having Children Until They Have a Girl
Each birth is independent, with probability 1/2 of being a girl.
CORE IDEA
50% girls
Every family ends with exactly one girl. Before that girl, there may be 0, 1, 2, 3, ... boys.
Girls / family1
Expected boys1
Expected size2
E[boys] = 0(1/2)+1(1/4)+2(1/8)+... = 1
Girl fraction = 1 / (1+1) = 1/2
Girl fraction = 1 / (1+1) = 1/2
POSSIBLE FAMILIES
G → 1 childP = 1/2B G → 2 childrenP = 1/4B B G → 3 childrenP = 1/8B B B G → 4 childrenP = 1/16⋮⋮
The stopping rule changes family size, not the probability that an individual birth is a girl.
INTERACTIVE SIMULATION
Watch the population ratio approach 50%
Families—
Girls—
Boys—
Girls among children—