In order to be continuous everywhere, we only need to satisfy continuity at . For that to happen, we need to have
By the function's definition, . Compute the limits:
So we must have
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2 answers:
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Answer:
eventually the gender ratio of population in this society will be 50% male and 50% female.
Step-by-step explanation:
For practical purposes we will think that every couple is healthy enough to give birth as much children needed until giving birth a girl.
As the problem states, "each couple continue to have more children until they get a girl and once they have a girl they will stop having more children". Then, every couple will have one and only one girl.
- This girl would be the n-th child with a probability
.
We will denote for P(Bₙ) the probability of a couple to have exactly n boys.
Observe that statement 1 implies that:
.
Then, the average number of boys per couple is given by
This means that in average every couple has a boy and a girl. Then eventually the gender ratio of population in this society will be 50% male and 50% female.