This question can be solved simply using the concepts of Baye's Theorem in conditional probability.
The following data is given: -
P(A) = 0.3, P(B | Ac) = 0.25 and P(B | A) = 0.45
From the given data, we can find out: -
P(Ac) = 1- P(A) = 1- 0.3 = 0.7
Also, P(B) = [P(A) x P(B | A)] + [P(Ac) x P(B | Ac)] = [0.3 x 0.45] + [0.7 x 0.25] = 0.135 + 0.175 = 0.31
Now, according to Bayes' Theorem: -
P(Ac | B) = [P(B | Ac) x P(Ac)] / P(B) = [0.7 x 0.25] / 0.31 = 0.175 / 0.31 = 0.564 ≈ 0.56
Therefore, the correct answer is Option (D).