A shopkeeper sells three types of flower seeds A1, A2 and A3. They are sold as a mixture, where the proportions are 4 : 4 : 2, respectively. The germination rates of the three types of seeds are 45%, 60% and 35%.
Calculate the probability:
a. of a randomly chosen seed to germinate.
b. that it will not germinate given that the seed is of type A3.
c. that it is of the type A2 given that a randomly chosen seed does not germinate.