Given p(x) = 0.5, p(y) = 0.4, and p(y|x) = 0.3, what are p(x and y) and p(x or y)?

Use the definition of conditional probability to find the "and" probability:

Use the inclusion/exclusion principle to find the "or" probability:

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.