Total probability and Bayes' theorem

Three software engineers A, B, C are being considered for selection as project leader. The probabilities of their selection are in the ratio $1:3:6$. If A is selected, the probability that she will use R software is $0.8$; the corresponding probabilities for B and C are respectively $0.5$ and $0.3$. Consider:

(I) The probability that R software will be used for the new project is $0.41$.
(II) If R software is used, the probability that either A or B is the project leader is $23/41$.