Case Study Problem:
A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold in the form of a mixture, where the proportions of these seeds are $4:4:2$, respectively. The germination rates of the three types of seeds are $45\%,60\%$ and $35\%$ respectively.
Based on the above information:
(a) Calculate the probability that a randomly chosen seed will germinate;
(b) Calculate the probability that the seed is of type A2, given that a randomly chosen seed germinates.