Let \( S=\{w_1,w_2,\ldots\} \) be the sample space of a random experiment. Let the probabilities satisfy \[ P(w_n)=\frac{P(w_{n-1})}{2},\qquad n\ge 2. \] Let \[ A=\{\,2k+3\ell : k,\ell\in\mathbb{N}\,\},\qquad B=\{\,w_n : n\in A\,\}. \] Then \(P(B)\) is equal to: