Answer is (B)
$P(A\cup B) = P(A) + P(B) - P(A\cap B)$
$= (1 - P(A')) + (1- P(B')) - P(A\cap B)$
$= \left(1-\dfrac{1}{3}\right) + \left(1-\dfrac{1}{3}\right) - \dfrac{1}{2}$
$=\dfrac{4}{3} - \dfrac{1}{2} =\dfrac{5}{6} =\dfrac{10}{12}.$
Here: If we simplify the option(B) we get $5/6.$