Decision_of_Uncertainty

Decision of Uncertainty Decision of Uncertainty University of Phoenix Decision I recently moved back to the United States (US) from Germany and I had to decide if I should continue to purchase full coverage auto insurance consisting of collision and comprehensive or only liability auto insurance. Due to a considerable decrease in pay returning back to the US, this could be a significant financial decision for my budget. Through my research, I realized the state of Georgia has a mandatory minimum amount of insurance one must purchase. The website Georgia Car Insurance Center states this includes $25,000 per person for bodily injury, $50,000 per accident for bodily injury to two or more people, and $25,000 per accident for property damage. I could purchase minimum liability coverage for $243.20 for the entire year, or I could purchase full coverage for $523.80 per year with deductibles for property damage, comprehensive, collision, rental reimbursement, and emergency road side service. I could save $280.60 per year by purchasing liability only. Research The website for the Georgia Department of Transportation (GDOT) (2006), there were over six million automobile accidents in Georgia from 2000 to 2006. According to GDOT an average of 873,000 people are involved in a motor vehicle crash each year out of a population of an estimated nine million. The Georgia Department of Revenue estimates around 12 percent of motorists are uninsured in the state. Full coverage can be purchased for only $280.60 more per year, should I purchase full coverage auto insurance' To make an informed decision, I researched the cost of automobile insurance and the likelihood of getting into an accident. My research data was from Georgia Department of Transportation and consisted of automobile statistics spanning seven years. Although I plan to travel a bit during the year, my primary use for the automobile is in Hinesville, Georgia which is Liberty County. Interpretation Once the research was gathered, I focused on accurately interpreting the data to make an accurate informed decision. The interpretation of data was completed using Bayes’ Theorem as the probability model. Bayes’ theorem shows the relation one conditional probability and its inverse. The key is that the probability of event A given event B depends on the relationship between A and B, and also the probability of A independent of B, and also the probability of B independent of A. Bayes’ theorem is best used to specify how an ideally rational person would respond to confidence levels for purchasing full coverage automobile insurance and predicting the occurrence of an automobile accident. While there are other effective analytical tools used to derive probability data such as hypothesis testing, Bayes’ theorem is more appropriate for this situation based on nature of the evidence. Part of statistical modeling is using the right analytical tool for the appropriate situation. After looking at the statistics, I found that there is a 10 % chance to be involved in an automobile accident. I then set up the variables to examine the probability of: Accident 1 = A1 = likelihood of accident happening Accident 2 = A2 = likelihood of accident not happening This helped me to determine if I needed to purchase full coverage or only liability insurance. I know that there is a 10 % chance to be involved in an auto accident (P(A1) . There is a 90 % chance not to be involved in an auto accident (P(A2). The Georgia Department of Revenue statistics show that there is a 12 % chance that (1,080,000) drivers will not have any insurance at all (B). So, B = drivers that don’t have any insurance. This is written as P(B|A1) = .12. Since I live in a rural area and travel on a highway that has quite a few deer, I am also concerned about being in an accident with a deer. According to the Georgia Department of Transportation, 17,460 drivers are in an accident with a deer. The probability of being hitting a deer is .002 or written as P(B|A2). The probability according to Bayes’ theorem shows us: P(A1|B) = P (A1) P (B|A1) P(A1) P(B|A1) + P (A2) P (B|A2) = (.10) (.12) = .012 (.10) (.12) + (.90) (.002) = .012 / .0258 = .47 Probability of getting into an accident .012 / .0258 = .47 Probability of not getting into an accident .0138 / .0258 = .53 Based on the above calculations, there is a .43 probability of getting into an accident and a .53 probability of not getting into an accident. Since decisions are based on the amount of personal risk we are willing to accept, statistical tools gives us a way to minimize that risk. Based on the above data, I would purchase full coverage insurance. References Georgia Car Insurance Center. (2010). Retrieved from http://www.dmv.org Georgia Department of Transportation. (2006). Retrieved from http://www.dot.state.ga Lind, D., Marchal, W., & Wathen, S. (2008). Statistical techniques in business and economics (13th ed.). Boston: McGraw-Hill/Irwin.