Me solve this probability problem, i don't understand conditional probability that well

A) (0.2x0.3) + (0.3x0.2) + (0.5x0.1) = 0.17
b) 0.3x0.8 = 0.24

Part a: 0.2*0.3+0.3*0.2+0.5*0.1= 0.17
Part b: You have to find the probability for NOT late and this is 1-prob of being late, then use Bayes' theorem. So you have 
(0.3*0.8)/(0.2*0.7+0.3*0.8+0.5*0.9)= 0.2892