Let E1,E2,E3 be three mutually exclusive events such that p(E1)=2+3p6,p(E2)=2−p8,p(E3)=1−p2. If the maximum and minimum value of P are P1&P2 then P1+P2=

0≤2+3p6≤1⇒p∈[−23,43]0≤2−p8≤1⇒p∈[−6,2]0≤1−p2≤1⇒p∈[−1,1]0∠ P(E1)+P(E2)+P(E3)≤1⇒P∈[23,263]⇒2/3≤p≤1∴p∈[23,1] ∴P1+P2=23+1=53

Let E1,E2,E3 be three mutually exclusive events such that p(E1)=2+3p6,p(E2)=2−p8,p(E3)=1−p2. If the maximum and minimum value of P are P1&P2 then P1+P2=

0≤2+3p6≤1⇒p∈[−23,43]0≤2−p8≤1⇒p∈[−6,2]0≤1−p2≤1⇒p∈[−1,1]0∠ P(E1)+P(E2)+P(E3)≤1⇒P∈[23,263]⇒2/3≤p≤1∴p∈[23,1] ∴P1+P2=23+1=53

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Let $E 1, E 2, E 3$ be three mutually exclusive events such that $p (E 1) = \frac{2 + 3 p}{6}, p (E 2) = \frac{2 - p}{8}, p (E 3) = \frac{1 - p}{2}$ . If the maximum and minimum value of P are $P 1 & P 2$ then $P 1 + P 2 =$

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$\frac{2}{3}$

$\frac{5}{3}$

$\frac{5}{4}$

$1$

answer is B.

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$0 \leq \frac{2 + 3 p}{6} \leq 1 \Rightarrow p \in [- \frac{2}{3}, \frac{4}{3}]$

$0 \leq \frac{2 - p}{8} \leq 1 \Rightarrow p \in [- 6, 2]$

$0 \leq \frac{1 - p}{2} \leq 1 \Rightarrow p \in [- 1, 1]$

$0 ∠ P (E 1) + P (E 2) + P (E 3) \leq 1 \Rightarrow P \in [\frac{2}{3}, \frac{26}{3}]$

$\Rightarrow 2 / 3 \leq p \leq 1$

$∴ p \in [\frac{2}{3}, 1] ∴ P_{1} + P_{2} = \frac{2}{3} + 1 = \frac{5}{3}$

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Let E1,E2,E3 be three mutually exclusive events such that p(E1)=2+3p6,p(E2)=2−p8,p(E3)=1−p2. If the maximum and minimum value of P are P1&P2 then P1+P2=

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Let $E 1, E 2, E 3$ be three mutually exclusive events such that $p (E 1) = \frac{2 + 3 p}{6}, p (E 2) = \frac{2 - p}{8}, p (E 3) = \frac{1 - p}{2}$ . If the maximum and minimum value of P are $P 1 & P 2$ then $P 1 + P 2 =$