JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 17

Let $E_1$, $E_2$, $E_3$ be three mutually exclusive events such that $P(E_1)=\dfrac{2+3p}6$, $P(E_2)=\dfrac{2-p}8$ and $P(E_3)=\dfrac{1-p}2$. If the maximum and minimum values of p are $p_1$ and $p_2$, then $(p_1+p_2)$ is equal to :