**Question:**

In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)

**Answer:**

“very simple”. Half the couples have boys first, and stop. The rest have a girl. Of those, half have a boy second, and so on.

So suppose there are N couples. There will be N boys.

1/2 have a boy and stop: 0 girls

1/4 have a girl, then a boy: N/4 girls

1/8 have 2 girls, then a boy: 2*N/8 girls

1/16 have 3 girls, then a boy: 3*N/16 girls

1/32 have 4 girls, then a boy: 4*N/32 girls

…

Total: N boys and

1N 2N 3N 4N

– + – + – + — +… = ~N

Therefore, the proportion of boys to girls will be pretty close to 1:1

plz clarify it litl bit more…

Lets consider number of couple are 1000…

at first half couple have boys means half couple have girls..

G=1000/2(Continues…), B=1000/2(Stops…)

at second half couple have boys means half couple have girls..

G=1000/2 + 500/2(Continues…) B=1000/2+500/2(Stops..)

and so on…

at the end ratio of boys to girls is 1:1…

Why are we assuming that at the first iteration, 0 girls would be produced? Isn’t it possible for 50% to be boys and 50% girls at the first step?

what if no couple got a boy 1st?

Does anyone second this logic??

Let n be the number of girls a family has, on average, before having a boy. Then, on average,

each family will have n girls and 1 boy –> The ratio of the country will be 1:n.

Family has a baby and there are two possible outcomes: 1) boy, 2) girl.

n is equal to the number of girls that they are likely to have in each case, divided by two (since each case will happen 1/2 of the time).

In the first case, the family has a boy and a likelihood of 0 of having more girls. In the second case, the family has a girl and a likelihood of n of having more girls. Therefore, in the second case we have n + 1 girls.

Therefore,

n = 1/2*(0) + 1/2*(1 + n)

–> n = (1+n)/2

–> 2n = 1+n

–> n = 1

Over time the country will have 1:n = 1:1 ratio of boys to girls.

Assume: N families

Therefore total number of boys: N

For each family, probability of Girl child: 0+(1/2)^1+(1/2)^2+(1/2)^3+….. =1(sum of infinte GP)

Therefore for N such family total number of girls: N

Ratio : N/N = 1:1