### statistical spookiness

**(?) (?)** Each of two balls is painted either black or gold and then placed in an urn.

Suppose that each ball is colored with a probability of 1/2 and that these

events are independent.

**(g?) (g?)** Suppose that you obtain information that the gold paint *has* been used (thus at least one ball is painted gold). Compute the conditional probability that

both balls are painted gold.

**(g) (?)** Suppose now that the urn tips over and 1 ball falls out. It is painted gold.

What is the probability that both balls are gold in this case?

I am going to just give you the answers:

**(?) (?) **1/4 probability with possibilities: b-b, b-g, g-b, g-g

**(g?) (g?)** 1/3 probability with possibilities: b-g, g-b, g-g

**(g) (?) **1/2 probability with possibilities: g-b, g-g

the trick is that going from the second to the third problem, one has been given more information because they have *seen* one of the balls, the same way quantum darwinianism describes collapsing quantum possibilities as it enters a classical environment. weird