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.