Question 1022485
Apply Bayes' Theorem directly:

P(1st box|blue) = P(1st box AND blue)/P(blue) = P(blue|1st box)*P(1st box)/P(blue) =  P(blue|1st box)*P(1st box)/[P(blue|1st box)*P(1st box) +  P(blue|2nd box)*P(2nd box)] = {{{((3/5)*(1/2))/((3/5)*(1/2)+(2/5)*(1/2)) = 3/5}}}.