What is P(B) equal to if A U B = sample space, P(A and BC) = 0.25, and P(Ac) = 0.35?

0.75.

The key is in the phrase aub = sample space that means that all the probabilities are contained in the a circle and the b circle. That also means that all probabilities in the two circles add to 1. If you draw two circles that intersect, then the part a and bc is the part of circle a that is not intersecting anything and that is 0.25. The part ac is the part of circle b that doesnt intersect with a. this is 0.35that leaves the intersection between the two circles. Since all probabilities add to 1, then the intersection is 1 - (0.25 + 0.35) = 0.4. so, p(b) = 0.4 + 0.35 = 0.75