Probability

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