Given two events \( A \) and \( B \). If odds against \( A \) are \...

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Given two events \( A \) and \( B \). If odds against \( A \) are
\( \mathrm{P} \)
\( 2: 1 \) and those in favour of \( A \cup B \) are as \( 3: 1 \), then
W
(1) \( \frac{1}{2} \) P(B) \( \leq \frac{3}{9} \)
(2) \( \frac{5}{12} \leq \mathrm{P}(\mathrm{B}) \leq \frac{3}{4} \)
(3) \( \frac{1}{2} \leq \) P (B) \( \leq \frac{3}{5} \)
(4) \( \frac{1}{3} \leq \) P (B) \( \leq \frac{3}{4} \)
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