You are planning an event and want to decide whether to do it at the park (outdoors) or inside the gym (indoors). The weather conditions are uncertain with a 60% chance of being a good weather, and 40% chance of being a bad weather. The below information are for the rental costs and expected revenues based on the weather condition: | Location | Rental Cost ($) | Good Weather Revenue ($) | Bad Weather Revenue ($) | | :--- | :--- | :--- | :--- | | Park (outdoors) | 2000 | 6000 | 1500 | | Gym (Indoors) | 1500 | 3000 | 4000 | You were able to construct the below decision tree. [Decision Tree Diagram] Location decision - park -> weather conditions - good -> (Probability 1) -> Outcome 1 - bad -> (Probability 2) -> Outcome 2 - gym -> weather conditions - good -> (Probability 3) -> Outcome 3 - bad -> (Probability 4) -> Outcome 4 a) What are the Probabilities and Outcomes in the Decision Tree? Show any calculations made. b) Use Bayes' Decision Rule to decide the location of the event. Show your work.
Added by Kimberly H.
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The expected payoff for each location is calculated as follows: - Expected payoff (Park) = (Probability 1 * Outcome 1) + (Probability 2 * Outcome 2) = (0.6 * $500) + (0.4 * $4500) = $300 + $1800 = $2100 - Expected payoff (Gym) = (Probability 3 * Outcome 3) + Show more…
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