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Decisions of Uncertainty

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Decision of Uncertainty Paper
QNT/561 Applied Business Research and Statistics
November 23, 2011

Decision of Uncertainty Paper
August of 2006 was memorable month for every citizen of El Paso area. That year record-breaking rainfall, which was twice the average annual destroyed more than 300 homes and caused 100 million dollars in damages. For days after the flood water subsided the area was still under threat of flooding because of the substandard drainage system and outdated levy system. This incident forced many El Pasoans to evaluate the possibility of the future flooding an estimate the cost of purchasing the flood insurance. According to the study performed by the National Weather Service Forecast Office Deep convection, which produces excessive rainfall and flash flooding, poses a threat to lives and property over south-central and southwestern New Mexico and far western Texas, primarily during the summer monsoon season. Forecasting these phenomena are difficult across this region due to the irregular terrain, the sparse data and the relatively poor performance of numerical models in the prediction of heavy rain across the southwestern United States (Rogash, 2003).
Therefore, we can safely assume the2006 flooding in El Paso area was a combination of independent variables such as topography and existing drainage system and independent variables such as weather patterns and rainfall. Some such as city representative Eddie Holguin called it a 500-year abnormality and assumed “we still have 490 more years to deal with this”( El Paso times, 2008) on the contrary to the National Weather Service, which assessed the probability of every 100 years. Considering the fact the probability of 500 year flood will not affect the current population I wanted to explore possibility of another flood happening within the next 100 years and whether it may substantiate my decision to purchase additional flood insurance.

The Bayes’ theorem is the method chosen by me to explore the relations between the conditional probabilities, such as a likelihood of another 100-year flood happening in El Paso area and the prospect the sewage system will not handle the amount of water in my decision whether to purchase the flood insurance. It allows me to relate the probability of one event to another and whether it is defined by the frequency of the event based on observations.
According to the gathered data the probability of the hundred-year flood recurring within any given year within this period is 1/100=0.01 so the probability another flood will not happen within the next hundred years is 0.99.
F1=another flood=0.01
F2=no flood=0.99
Consequently P (F1) = 0.01 and P (F2) = 0.99, which applies only to the major flooding, such as in 2006. Additional data provided by the City Council states also the 80% of the city’s sewage system is not design to support the rains of this magnitude –M. That leaves 20% probability the existing run off system will be sufficient to handle monsoon rain (Engineering and Construction Management, 2011). This additional data can be written as P (M|F1) = 0.80 where the flooding will occur because of flash flood and P (M|F2) = 0.23 where the flooding will not be present.
According to the Bayes’ theorem P (F1) P (M|F1)
P (F1|M) = _________________________

P (F1) P (M|F1) + P (F2) P (M|F2)

Therefore:

* (0.80)
P (F1|M) = _________________________ = 0.08 = 0.3394

(0.01) (0.80) + (0.99) (0.23) 0.2357

Based on that information there is a 0.0394 probability the flooding will occur in the area with insufficiently developed sewage system. Presence of the inferior sewage system in the area raised the possibility of flooding from 0.01 to 0.2357.

Event | Prior ProbabilityP (F1) | Conditional ProbabilityP (M|F1) | Joint ProbabilityP (F1 and M) | Posterior ProbabilityP (F1|B) | Flooding | 0.01 | 0.80 | 0.008 | 0.008/0.2357 = .0.033 | No Flooding | 0.99 | 0.23 | 0.2277 | 0.2277/0.2357 = 0.967 | | | | P(B) = 0.2357 | = 1.00 |

Based on those calculations there is a 0.03 probability the floods will be caused by the rain and substandard sewage and levy system versus 0.96 probabilities they will not happen.
According to the Farmers Insurance Group the average rates for the flood insurance in Texas, which covers the building worth 200,000 $ and the contents up to 80,000 $ costs 296$ (Texas Flood Insurance, 2011). Without that additional coverage the homeowners can otherwise count only on the president announcing the county as a federal disaster area. Based on the low probability of the flood affecting the El Paso area I have decided not to purchase the additional flood insurance because of the relatively small chance of occurrence versus the additional cost.

Reference
Engineering and Construction Management. (2011). El Paso City Floodplain Services. Retrieved from http://www.elpasotexas.gov/engineering/floodzones.asp#City Floodplain Services
Rogash, J. (2003). Meteorological Aspects of South-Central and Southwestern New Mexico and Far Western Texas Flash Floods. Retrieved from http://www.srh.noaa.gov/images/epz/research/flashflood.pdf
Texas Flood Insurance. (2011). Retrieved from https://www.texas-flood-insurance.com/thanks.html

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