the pilot and wait for the streaming service's decision $or$ transfer the rights for the pilot and series $to$ a competitor for $$100,000.$ Hale's decision alternatives and profits $(in$ thousands $of$ dollars$)$ are $as$ follows:

$\begin{array}{cc}\text{D}\text{e}\text{c}\text{i}\text{s}\text{i}\text{o}\text{n}\text{A}\text{l}\text{t}\text{e}\text{r}\text{n}\text{a}\text{t}\text{i}\text{v}\text{e}& \text{S}\text{t}\text{a}\text{t}\text{e}of\text{N}\text{a}\text{t}\text{u}\text{r}\text{e}\\ ?& ?\\ ?& ?\\ \text{R}\text{e}\text{j}\text{e}\text{c}\text{t}& s_1\\ 1\text{Y}\text{e}\text{a}\text{r}& s_2\\ 2\text{Y}\text{e}\text{a}\text{r}\text{s}& s_3\\ \text{P}\text{r}\text{o}\text{d}\text{u}\text{c}\text{e}\text{p}\text{i}\text{l}\text{o}\text{t}& d_1\\ -100& 50\\ 150& ?\\ \text{S}\text{e}\text{l}\text{l}to\text{c}\text{o}\text{m}\text{p}\text{e}\text{t}\text{i}\text{t}\text{o}\text{r}& d_2\\ 100& 100\\ 100& ?\end{array}$

result $in$ a favorable $(F)oran$ unfavorable $(U)$ review and that the following probabilities are relevant.

$P(F)=0\mathrm{.}69$

$P(U)=0\mathrm{.}31$

$P(s_1|F)=0\mathrm{.}08$

$P(s_2|F)=0\mathrm{.}28$

$P(s_3|F)=0\mathrm{.}64$

$P(s_1|U)=0\mathrm{.}45$

$P(s_2|U)=0\mathrm{.}39$

$P(s_3|U)=0\mathrm{.}16$

$(a)$ Construct a decision tree for this problem. $(Enter$ your answers $in$ thousands $of$ dollars.$)$