Rain (Local is wrong, Federal is right):
$P(\text{L wrong, F right}) = (1/3)(3/4)$
$P(\text{L wrong, F right}) = 1/4$
No rain (Local is right, Federal is wrong):
$P(\text{L right, F wrong}) = (1/4)(2/3)$
$P(\text{L right, F wrong}) = 1/6$
$P(\text{rain OR no rain}) = 1/4 + 1/6$
$P(\text{rain OR no rain}) = 5/12$
$P(\text{rain}) = \dfrac{1/4}{5/12}$
$P(\text{rain}) = 3/5$ ← answer
