Given:
[tex]P(A)=\frac{1}{3}\text{ ; P(B)=}\frac{2}{5}\text{ ; P(A}\cup B)=\frac{3}{5}[/tex][tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex][tex]\begin{gathered} \frac{3}{5}=\frac{1}{3}+\frac{2}{5}-P(A\cap B) \\ P(A\cap B)=\frac{1}{3}+\frac{2}{5}-\frac{3}{5} \\ P(A\cap B)=\frac{5+6-9}{15} \\ P(A\cap B)=\frac{2}{15} \end{gathered}[/tex]
Option D is the final answer.
