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## Boys and Girls 4

To help solve an acute national over-population problem, a government issues a radical decree that families must stop having children as soon as they have had one son. After a while, there are some families with only one boy, some with one girl and one boy, some with two girls and one boy, some with three girls and one boy, some with six girls and one boy, etc., and some families only have girls and give up trying for a son.

Would boys tend to outnumber girls in this generation? Or vice versa?

neither

Regardless of the decrees issued by the government, the ratio of boys to girls born is unchanged. Whoever the next mother in the country to give birth is, she always has a 50-50 chance of boy or girl.

Tarun245

its still 50-50 chance

Vishal barot

Good one, It is a lateral thinking question

Alejandro Morales

I was going to question this until I did the math, lol no wonder stats is not my strong when it comes to math. The logic initially makes you think is the girls but then you do it and you find that it is a different solution. Good problem.

Nigel Parsons

It does seem to need further consideration, but the basis of 50/50 is true.

For those still unsure, start with 128 couples trying for families. The chances are (allowing for slight deviations from the norm) that 64 couples will have boys, and have to cease reproduction, the other 64 will have girls, and may choose to continue, but at this stage the score is 64 all.

The 64 families who choose to continue can expect to produce 32 boys & 32 girls. Again we have an equal number, and 32 families who can choose to carry on. Continuing this, we can expect (if everyone continues having children for as long as they are permitted) that the 128 families will end up with 128 boys & 128 girls, just some families will be smaller than others.

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