In a certain selection of flower seeds have been treated to improve germination and have been left untreated. The seeds which have been treated have a probability of germination of 0.8, whereas the untreated seeds have a probability of germination of 0.5.

(a) Find the probability that a seed, selected at random, will germinate. The seeds were sown and given time to germinate.

(b) Find the probability that a seed selected at random had been treated, given that it had germinated. (L)