Mental_floss has a list of ten paradoxes, dealing with math, logic, physics, language, or some other method of cramping your brain. There’s the crocodile who grabs a kid, a race with a tortoise, the dehydrated potatoes, and this one:
3. THE BOY OR GIRL PARADOX
Imagine that a family has two children, one of whom we know to be a boy. What then is the probability that the other child is a boy? The obvious answer is to say that the probability is 1/2—after all, the other child can only be either a boy or a girl, and the chances of a baby being born a boy or a girl are (essentially) equal. In a two-child family, however, there are actually four possible combinations of children: two boys (MM), two girls (FF), an older boy and a younger girl (MF), and an older girl and a younger boy (FM). We already know that one of the children is a boy, meaning we can eliminate the combination FF, but that leaves us with three equally possible combinations of children in which at least one is a boy—namely MM, MF, and FM. This means that the probability that the other child is a boy—MM—must be 1/3, not 1/2.
Wait a minute, I’ve flipped enough coins in statistics class to know that the real answer is still 50%, but how in the world did they come up with 1/3? Wait, wait: just who said these were “equally possible combinations”?
Still, debunking that one was easy compared to some of the other paradoxes in the list at mental_floss.
(Image credit: Flickr user Alex Proimos)