(?) (?) 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