Thursday November 29, 2012

### Coin flip example

“If a woman has two children and one is a girl, the chance that the other child is a girl has to be 50-50, right? No.”

I figured this out. Go back to the coin example. I flip two coins into a box, such that I can see the results and you can’t. The probability of two heads is 1 in 4. The probability of two tails is 1 in 4. But since there are two ways to get one heads and one tails, the probability of one coin being heads and the other being tails is 1 in 2.

I look down, and I say, “one of the coins is heads.” At this point, the probability of the other coin being heads is 1 in 3, and the probability of the other coins being tails is 2 in 3.

Back to the example of the kids. If I said “the woman’s first child is a girl.” Then the probability of her second child being a boy would be 50-50.

I think what this highlights is the extent to which what our brains are good for is based on how we evolved. We’re wired to figure out certain real-world practical problems, and comparatively terrible at abstract thought. We have the illusion of being good at abstract thought. Simple puzzles like this poke holes in the illusion.

(Via Steve, who brought an old newspaper clipping with this.)

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