Question 1048696
What you originally have for part (a), delete it.  What you have for part (b), put it under part (a).  That will make it correct, by Bayes' Rule and the rule of total probability.


(b)
P(A'|B')  =P(A'∩B')/P(B') = P((A∪B)')/(1-P(B)) = (1-P(A∪B))/(1-P(B))

= (1-P(A)-P(B) +P(A∩B))/(1-P(B))

= {{{(1-1/200-0.05425+0.0045)/(1-0.05425)  = 3781/3783 = 99.9}}} (nearest tenth of a percent.)