Suppose \( E_{1}, E_{2} \) and \( \mathrm{E}_{3} \) be three mutually exclusive events
\( \mathrm{P} \) such that \( \mathrm{P}(\mathrm{Ei})= \) pi for \( i=1,2,3 \).
W \( \mathrm{P}\left(\mathrm{E}_{1} \cap \overline{\mathrm{E}}_{2}\right)+\mathrm{P}\left(\mathrm{E}_{2} \cap \overline{\mathrm{E}}_{3}\right)+\mathrm{P}\left(\mathrm{E}_{3} \cap \overline{\mathrm{E}}_{1}\right) \) equals
(1) \( p\left(1-p_{2}\right)+p_{2}\left(1-p_{3}\right)+p_{3}\left(1-p_{1}\right) \)
(2) \( p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{1} \)
(3) \( p_{1}+p_{2}+p_{3} \)
(4) None of the above
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