A pot at the end of the rainbow has one gold coin, two silver coins, and one bronze coin. If a coin is selected at random, and it is not gold, the process is stopped. If the coin is gold, the coin will be kept back in the pot, and then another coin is picked randomly again, and then the process stops. For this process, a person can pick either one or two coins. A represents the quantity of gold coins chosen, and B represents the quantity of silver coins chosen.

a. Give a table showing the joint probability mass function of A and B, pA,B(a,b).

b. Give the conditional probability mass function of B, if A = 0.

c.Establish whether A and B are independent or not, justifying your answer using math.