One bag contains 15 identical (in shape) coins - nine of silver and six of gold. A second bag contains 16 more of these coins - six silver and 10 gold. Bruno reaches in and selects one coin from the first bag and then places it in the second bag. Then Madeleine selects one coin from this second bag.
(a) What is the probability Madeleine selected a gold coin?
(b) If Madeleine's coin is gold, what is the probability Bruno had selected a gold coin?