Question

In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

Answer 1

So there's a way to figure this out using really advanced math, but here's the "practical" way to figure it out. 

Let's say you have 16 couples in this hypothetical population. If each couple had 1 child in the first iteration, each family would have a 50% chance of having a girl and a 50% chance of having a boy. As the odds are 50/50 you could create a visual by simply alternating boy/girl/boy/girl. It would look like this:
B
G
B
G
B
G
B
G
B
G
B
G
B
G
B
G

Only those families who had girls would then go on to the second round, and once again they would have a 50/50 chance of having either a boy or a girl, so for each family that had a girl you can again alternate boy/girl/boy/girl. This second iteration would look like this:
B
GB
B
GG
B
GB
B
GG
B
GB
B
GG
B
GB
B
GG

During the third iteration, only those who had 2 girls in their previous iterations would continue having children. Again there would be a 50/50 chance of either a boy or a girl, so you could again alternate boy/girl/boy/girl. The third iteration would look like this:
B
GB
B
GGB
B
GB
B
GGG
B
GB
B
GGB
B
GB
B
GGG

In a 16 couple population this pattern would repeat two more times in a 4th and 5th iteration -
4th Iteration:
B
GB
B
GGB
B
GB
B
GGGB
B
GB
B
GGB
B
GB
B
GGGG

5th Iteration:
B
GB
B
GGB
B
GB
B
GGGB
B
GB
B
GGB
B
GB
B
GGGGB

If you count up the number of boys and girls you'll see there are 16 boys and 15 girls. With a larger sample size (millions in the case of a real country) you'd find that the ratio of boys to girls is 1:1.