Let E_1, E_2, E_3 be three mutually exclusive events such that P ( E_1)=(2+3 p)/6, P ( E_2)=(2- p)/8 and P ( E_3)=(1- p)/2. If the maximum and…

Let $\displaystyle \mathrm{E}_1, \mathrm{E}_2, \mathrm{E}_3$ be three mutually exclusive events such that $\displaystyle \mathrm{P}\left(\mathrm{E}_1\right)=\frac{2+3 \mathrm{p}}{6}, \mathrm{P}\left(\mathrm{E}_2\right)=\frac{2-\mathrm{p}}{8}$ and $\displaystyle \mathrm{P}\left(\mathrm{E}_3\right)=\frac{1-\mathrm{p}}{2}$. If the maximum and minimum values of p are $\displaystyle \mathrm{p}_1$ and $\displaystyle \mathrm{p}_2$, then $\displaystyle \left(\mathrm{p}_1+\mathrm{p}_2\right)$ is equal to :