>>13115666cosider G1 and G2 your first and second choice respectively, being 0 if the ball you picked was silver and 1 if it was Gold.
what you're trying to find is P(G2 | G1) which means the probability of G2 being 1 if you know G1 is 1.
This is given to us by the following
P(G2 | G1) = P(G2 and G1) / P(G1)
the probability of G1 and G2 both being true is 1/3 since only the first box satisfies it.
the probability of G1 itself is 1/2 obviously.
then, P(G2 | G1) = P(G1 and G2)/P(G1) =
(1/3)/(1/2) = 2/3
