Man finds large canvas bag floating in river containing a body. Preliminary investigation cannot determine the victim's sex, race, or age. Presenters analyze the case using classical probability methods to predict victim and offender profiles based on FBI crime statistics. Forensic analysis later reveals the victim was a white female, contradicting the predicted victim profile of a white male. The presenters update their analysis and predict there is a 75.7% probability the offender is a white male based on the victim's characteristics. They provide an "official offender profile posting" seeking a white male as a person of interest.

1. THE BODY IN THE BAG Presenters: Dina Gaughan, Megan Poole, & Amy Shuleski February 24, 2010 MBA 512

2. Man Finds large canvas bag floating in river Preliminary investigation reveals body Sex/Race/Age Unknown Body in the Bag

3. Victim and Offender – Adults over 18yrs of age Victim/Offender Relationships 2003 Uniform Crime Reports – FBI http://www.fbi.gov/ucr/03cius.htm Analysis Profiles Victim Offender Joint Waiting on Forensics Analysis Identify Preliminary Profile

8. P (A or B) = P (A) + P (B)

9. Multiplication Rule

10. P (A&B) = P (A) * P (B)Probability Formulas

11. (Classical Method) Race: White: 3,562 / 6,911 51.5% Black: 3,098 / 6,911 44.8% Other: 195 / 6,911 2.8% Unknown: 56 / 6,911 .8% Sex: Male: 4,987 / 7,024 71% Female: 1,962 / 7,024 27.9% Unknown: 75 / 7,024 1.1% Victim Profile Prediction

12. (Addition Rule) White or Black =(3562/6911) + (3098/6911) = 96.4% Male or Female =(4987/7024) + (1962/7024) = 98.9% Victim Profile Prediction

13. (Multiplication Rule) White & Male =(3562/6911) * (4987/7024) = 36.6% White & Female =(3098/6911) * (1962/7024) = 14.4% Black & Male =(3098/6911) * (4987/7024) = 31.8% Black & Female =(3098/6911) * (1962/7024) = 12.5% Victim Profile Prediction

14. Victim Profile Prediction

15. (Classical Method) Race: White: 3,323 / 6,911 48.1% Black: 3,412 / 6,911 49.4% Other: 176 / 6,911 2.5% Unknown: 56 / 6,911 0.8% Sex: Male: 6,220 / 7,024 88.6% Female: 691 / 7,024 9.8% Unknown: 113 / 7,024 1.6% Offender Profile Prediction

16. (Addition Rule) White or Black =(3323/6911) + (3412/6911) = 97.5% Male or Female =(6220/7024) + (691/7024) = 98.4% Offender Profile Prediction

17. (Multiplication Rule) White & Male = (3323/6911) * (6220/7024) = 42.6% White & Female =(3323/6911) * (691/7024) = 4.7 % Black & Male =(3412/6911) * ( 6220/7024) = 43.7% Black & Female =(3412/6911) * (691/7024) = 4.9% Offender Profile Prediction

18. Offender Profile Prediction

20. White: .515 x .481 24.8%

21. Black: .448 x .494 22.1%

22. Other: .028 x .025 .1%

23. Likelihood of Victim & Offender same sex:

24. Male: .71 x .88 62.9%

25. Female: .279 x .098 2.7%

26. Unknown: .011 x .016 .02%Joint Profile Prediction

28. Male: 62.9% (Agrees with above prediction)Profile Predictions

29. No Identification Autopsy In water for 2 weeks Forensics Information Recovered White Female Blonde Hair Mid 30’s No children No jewelry Forensics Analysis - Victim

30. Victim Profile Probability did not match the Forensic Analysis Analysis Determined White Female Probabilities White Male – 36.6 % White & Female - 14.4% Forensics Analysis - Victim

31. Based on Victim’s Race – Likelihood Offender is: White 3,017/3,562 = 84.7 % Black 501/3,562 = 14.1 % Other 44/3,562 = 1.7 % Offender Profile Posting

32. Based on Victim’s Sex– Likelihood Offender is: Male 1754/1962 = 89.4 % Female 185/1962 = 9.4 % Unknown 231/1962 = 1.2 % Offender Profile Posting

33. (Multiplication Rule) White and Male .847 * .894 = 75.7 % Probability that the Offender is White and Male is 75.7 % Official Offender Profile Posting

34. Have you seen this man?If so, dial 911 White Male Questions?