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 :
JEE · Math · previous-year question
- A.$$\frac{2}{3}$$
- B.$$\frac{5}{3}$$correct
- C.$$\frac{5}{4}$$
- D.1
Answer
B. $$\frac{5}{3}$$
Explanation
$$0 \le {{2 + 3P} \over 6} \le 1 \Rightarrow P \in \left[ { - {2 \over 3},{4 \over 3}} \right]$$ $$0 \le {{2 - P} \over 8} \le 1 \Rightarrow P \in [ - 6,2]$$ $$0 \le {{1 - P} \over 2} \le 1 \Rightarrow P \in [ - 1,1]$$ $$0 $$0 $$P \in \left[ {{2 \over 3},{{26} \over 3}} \right]$$ Taking intersection of all $$P \in \left[ {{2 \over 3},1} \right)$$ $${P_1} + {P_2} = {5 \over 3}$$
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