John and Mario, owners of Mi Casa Front Porch Restaurant are planning a big Super Bowl event for their Glendale Westgate restaurant location and have received a permit for additional outside seating. They are debating on whether to invest in a tent for the event in case of rain. Because of demand for rentals, the cost to rent a tent of the size required is $30,000. Based upon the almanac, it only rained 15 days each year. Unfortunately, the long term forecast is for rain on Super Bowl Sunday; and this particular weatherman is correct 85% of the time. That also means that when it does not rain, he incorrectly forecasts rain 15% of the time. Using Bayes Theorem, determine the probability for rain and apply the probability to the decision to rent a tent.
Answer the question below in essay format. Your essay must include an introduction, a body, and a conclusion, and it must address all relevant parts of each question. Your response should be a minimum of 150 words in length and should include your analysis of the probability calculations. Make sure to cite any source you use. Proper citation format for a source includes the name of the author(s), the title of the work, the date of the publication, and the page number if you directly quote the source.
Essay Question
Based on the scenario above, calculate and interpret the probability using the Bayes Theorem and analyze the results for application to the business decision.