We have two urns. You can't tell them apart from the outside, but one has seven $1 chips and three $10 chips, and the other has nine $1 chips and one $10 chip. You randomly draw a chip from one of the urns and it happens to be a $10 chip. Without replacing this draw, I offer you a chance to draw and keep a chip from either urn. Should you draw from the same urn or the opposite urn, and what is the expected value of the chip you draw? Why?