Presumably, whatever is drawn from Urn I is independent of what is drawn from Urn II. This means
[tex]P(\text{red from Urn 1 AND red from Urn 2})=P(\text{red from Urn 1})\cdot P(\text{red from Urn 2})[/tex]
We have
[tex]P(\text{red from Urn 1})=\dfrac4{10}=\dfrac25[/tex]
[tex]P(\text{red from Urn 1})=\dfrac7{15}[/tex]
so the probability of drawing red balls from both urns is [tex]\dfrac25\cdot\dfrac7{15}=\dfrac{14}{75}[/tex]
