Each couple can give birth to as many children as they want until they have one doughter?
And the question is if there will be more girls or boys?
Without having a proof by probability I'd say there are more boys
Even though they have a chance to give birth to 10 boys or so before they get a girl, if we assume a probability of 50% for each outcome and if we assume that each couple will give birth to a doughter, 100% of couples will have a girl. The number of girls and boys before the law are even if we assume that the city only had couples.
So of all couples we'd expect about 50% to only give birth to one child which would be a girl. Half of the rest we'd expect to give birth to one boy and one girl which would cancel out again.
So only 1/4 of the couples we'd expect to have a positive boy-girl proportion.
So if we calculate the probability for one couple
it's: 1 for the girl and 11/2+21/4+3*1/8... (this sequence aproaches 2) for boys and so the ratio between girls and boys is expected to be about 1:2 and so we expect twice as many boys as girls.
Nice shot, yet the answer is incorrect :)
But I understood the task correctly?
And if so is it ok to assume a 1:1 chance for boy:girl?
Do we have to find the exact ratio we'd expect or is a proof which gender is more often enough?
You understood the problem right.
And the assumption is correct.
Just the final calculation wrong :)