Couples can have any number of sons, and every couple has exactly one daughter. Still, the accepted mathematical solution is an equal gender ratio for the couples' children.
In contrast, "0 sons" is going to describe a full half of all marriages.
So number of expected daughters = 1, number of expected sons = 1. In practice since women can't have an infinite number of children, then this wouldn't be an infinite series, so the real number of expected boys would be lower than one, but there you go…
Now, for the bus case, you get +1 if your bus turns up first, and -1 for every other bus that turns up first. Assume that it is completely random, then: expected + score is: 1/2 1 expected - score is: 1/2 * -1 + 1/4 * -2 + …
Expected + is 0.5, expected - is -1.
> 1 when your bus turns up, -1 for every bus going the other way.
>E[X]/E[Y] = E[X/Y] is not a valid identity.
is completely irrelevant here because it is being used to point out that a non-answer is wrong.