We have a total of 8 cards, where 3 of them are a multiple of 2, and 5 is an odd number. Consider that event A represents the probability of picking an odd number and event B is picking a multiple of 2. We know that the events are independent (because we put the cards back), therefore the probability of A and B can be expressed as
[tex]P(A\text{ and }B)=P(A)\cdot P(B)[/tex]Where
[tex]\begin{gathered} P(A)=\frac{5}{8} \\ \\ P(B)=\frac{3}{8} \end{gathered}[/tex]Therefore
[tex]P(A\text{ and }B)=\frac{5}{8}\cdot\frac{3}{8}=\frac{15}{64}[/tex]The final answer is
[tex]P(A\text{ and }B)=\frac{15}{64}[/tex]