Let E₁, E₂, E₃ be three mutually exclusive events such that P(E₁)=(2+3 p)/6, P(E₂)=(2-p)/8 and P(E₃)=(1-p)/2. If the maximum and minimum values of p are p₁ and p₂, then (p₁+p₂) is equal to:

Statistics and Probability: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jul, Morning shift · Q5022

JEE Main 202226 Jul, Morning shiftMathematicsMediumStatistics and Probability258× since 2002

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 :