The entries in a two-by-two determinant \( \left|\begin{array}{ll}a...

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The entries in a two-by-two determinant \( \left|\begin{array}{ll}a & b \\ c & d\end{array}\right| \) are integers that are chosen randomly and independently,
\( \mathrm{P} \)
W and, for each entry, the probability that the entry is odd is \( \mathrm{p} \). If the probability that the value of the determinant is even is \( 1 / 2 \), then find the value of \( p \).
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