By the inclusion/exclusion principle,
[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]
[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]
[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]
[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]
