imc

For the product of two numbers to be greater than zero, they either have to both be negative or both be positive. The interval for a positive number is $\frac{1}{3}$ of the total interval, and the interval for a negative number is $\frac{2}{3}$. Therefore, the probability the product is greater than zero is $$\frac{1}{3}\times \frac{1}{3}+\frac{2}{3}\times \frac{2}{3}=\frac{1}{9}+\frac{4}{9}=\boxed{\frac{5}{9}}$$