Solution
= Solution
{c}
Use $q=1/2$ and discount one step by $R=1.1$. At the up node, $A_1=110$ and immediate exercise pays $5$. Continuation is worth $(0+5/3)/(2R)=25/33<5$. At the down node, $A_1=100$ and immediate exercise pays $15$, while continuation is $(25/3+15)/(2R)=350/33<15$. Thus the <American put option> should be exercised at either time-one node, and
$$
\boxed{V_1=\begin{cases}5,&S_1=120,\\15,&S_1=100.\end{cases}}
$$