A shopkeeper sells three types of flower seeds `A_(1), A_(2)`, and `A_(3)`. They are sold as a mixture, where the proportions are 4:4:2 respectively. The germination rates of the three type of seeds are 45%, 60% and 35%. Calculate the probability
(i) Of a randomly chosen seed to germinate
(ii) That it will not germinate given that the seed is of type `A_(3)`.
(iii) That it is of the type `A_(2)` given that a randomly chosen seed does not germinate.

Answer

(i) 0.49, (ii) 0.65, (iii) 0.314