Question: Two gold, two silver and two copper coins are randomly divided between two people, so that each person receives three coins of unknown type. Then,

Two gold, two silver and two copper coins are randomly divided between two people, so that each person receives three coins of unknown type. Then, each person is required to return one coin of their choice back, but it can't be a copper coin. Naturally, when there is a choice, each person will return a coin with the lowest possible value. Let A be the event that both gold coins go to the same person when the coins are divided. Let B be the event that one person returns a silver coin and the other person returns a gold coin.

Question 1: P(A)=?

Question 2: P(A|B)=?

Question 3: Are events A and B independent?

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