Given that events A and B are independent.
It follows that the probability of the occurrence of both events is equal to the product of occurrence of each event independently,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]According to the given problem,
[tex]\begin{gathered} P(A)=\frac{1}{2} \\ P(B)=\frac{1}{3} \end{gathered}[/tex]Substitute the values,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]