A Construction Company Must Decide on the Size of the Shopping

A construction company must decide on the size of the shopping mall, i.e. Large, Medium or Small, that has to be constructed in their acquired plot in the sub-urban area of Seattle. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low. The level of response and the size of the mall will decide the return of investment from the mall. The profit payoff table for management (in millions of dollars) after 5 years is provided below.
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​ $$\begin{array} { | c | c | c | c | } \hline && { \text { Number of Visitors } } \\\hline \text { Size of the Mall } & \text { High } & \text { Moderate } & \text { Low } \\\hline \text { Large } & 25 & 15 & - 20 \\\hline \text { Medium } & 20 & 12 & - 10 \\\hline \text { Small } & 15 & 13 & 5 \\\hline\end{array}$$ ​
The probabilities for the state of nature are P(High) = 0.35, P(Moderate) = 0.40, and P(Low) = 0.25.
a. A test market study of the potential response for the mall in that area is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:
P(F|High) = 0.35; P(U|High) = 0.65
P(F|Moderate) = 0.45; P(U|Moderate) = 0.55
P(F|Low) = 0.20; P(U|Low) = 0.80
What is the probability that the market research report will be favorable?
b. Show the decision tree for this problem.