>>10972136Because Box 1 is more likely than Box 2.

I know it's counter-intuitive, so let's change the problem a little bit. Let's say Box 1 has 50 gold balls, and Box 2 has 49 silver balls and 1 gold ball. You pick one of them at random and extract a ball, and it's a gold ball. If you had to guess, would you say the box you picked was Box 1 or Box 2?

My first instinct was also to say 1/2, but 2/3 is correct. Our intuition on statistics is fucked up.