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  4. Let E1, E2, E3 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 minimum values of p are p 1 and p 2, then ( p 1+ p 2) is equal to :

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Q. Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P \left( E _1\right)=\frac{2+3 p }{6}$, $P \left( E _2\right)=\frac{2- p }{8}$ and $P \left( E _3\right)=\frac{1- p }{2}$. If the maximum and minimum values of $p$ are $p _1$ and $p _2$, then $\left( p _1+ p _2\right)$ is equal to :

JEE MainJEE Main 2022Probability - Part 2

Solution:

$ 0 \leq P \left( E _i\right) \leq 1 \text { for } i =1,2,3 $
$ \Rightarrow-2 / 3 \leq p \leq 1 $
$ E _1 \& E _2 \& E _3 $ are mutually exclusive
$ P \left( E _1\right)+ P \left( E _2\right)+ P \left( E _3\right) \leq 1$
$\Rightarrow 2 / 3 \leq p \leq 1 $
$p _1=1, p _2=2 / 3 $
$ p _1+ p _2=5 / 3$