\(B_2(E)=B_2^1(E)=\{w_2,w_5,w_3,w_6\}\). In particular, note that at \(w_6\), the agent believes (with probability 1) that \(E\) is true, but does not know that \(E\) is true as \(\Pi_2(w_6)\not\subseteq E\). So, there is a distinction between states the agent considers possible (given their “hard information”) and states to which players assign a non-zero probability.