A and B are events with Pr[A] = 0.25, Pr[B] = 0.32, and Pr[A ∩ B] = 0.06.
I assumed B' means the complement of B. A is the union of the two disjoint events A ∩ B', A ∩ B and so Pr[A] = Pr[A ∩ B'] + Pr[A ∩ B]. Pr[A|B'] = Pr[A ∩ B'] / Pr[B'], from the definition of conditional probability = (Pr[A] - Pr[A ∩ B]) / (1 - Pr[B]), since Pr[A] = Pr[A ∩ B'] + Pr[A ∩ B] = (0.25 - 0.06) / (1 - 0.32) = 0.19/0.68 = 19/68
by multiplying with 100% we get = 27.94%
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