Let \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) be three mutu...

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Let \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) be three mutually exclusive events
\( \mathrm{P} \) such that \( \mathrm{P}(\mathrm{A})=p_{1}, \mathrm{P}(\mathrm{B})=p_{2} \) and \( \mathrm{P}(\mathrm{C})=p_{3} \). Then,

W.
Let \( p_{1}=\frac{1}{2}(1-p), p_{2}=\frac{1}{3}(1+2 p) \) and \( p_{3}=\frac{1}{5}(2+3 p), p0 \) then \( p \) belongs to
(1) \( \phi \)
(2) \( (-1,2) \)
(3) \( \left(-1, \frac{1}{47}\right) \)
(4) \( \left(-\frac{1}{3}, \frac{2}{3}\right) \)
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