\(B_1^{\frac{1}{2}}(E)=\{w \mid p_0(E \mid \Pi_1(w))=\frac{p_0(E\cap\Pi_1(w))}{p_0(\Pi_1(w))}=\frac{1}{2}\}=\{w_1,w_2,w_3\}\): “Ann assigns probability 1/2 to the event \(E\) given her information cell \(\Pi_1(w_1)\).