(b) \(\frac{1}{4}\)
Since P(A) and P(B) are two mutually exclusive and exhaustive events , P(A) + P(B) = 1
\(\Rightarrow\) P(A) + 3 P(A) = 1
\(\Rightarrow\) 4 P(A) = 1 \(\Rightarrow\) P(A) = \(\frac{1}{4}\)
\(\Rightarrow\) P(B) = 1- \(\frac{1}{4}\) = \(\frac{3}{4}\)
\(\Rightarrow\) P(\(\bar B\)) = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\).