Let a, b, c ∈{1,2,3,4}. If the probability, that a x^2+2 √ 2 b x+ c >0 for all x ∈ R, is m/n, gcd ( m, n )=1, then m + n is equal to ____.

Let $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c} \in\{1,2,3,4\}$. If the probability, that $\displaystyle \mathrm{a} x^2+2 \sqrt{2} \mathrm{~b} x+\mathrm{c}>0$ for all $\displaystyle x \in \mathbf{R}$, is $\displaystyle \frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\displaystyle \mathrm{m}+\mathrm{n}$ is equal to $\displaystyle \_\_\_\_$.