The late spring morning broke along the banks of a river. Robert Donkin, an elderly retiree with fishing pole in hand, slipped through the underbrush that lined the river's banks. As he neared the shore, he saw a rather large canvas bag floating in the water, held by foliage that leaned over the river. The bag appeared to be stuffed, well-worn, and heavily stained. Upon closer inspecting, Mr. Donkin observed what he believed to be hair floating through the bag's opening. Marking the spot of his discovery, the fisherman fetched the authorities.

Preliminary investigation at the scene revealed a body in the bag. Unfortunately, it was impossible to identify the corpse's sex or race immediately. Estimating age was also out of the question. Forensics was assigned the task of identifying the victim and estimating the cause and time of death.

Part 1: While waiting for the forensics analysis, you as the detective in charge, have gathered the information shown in the included tables, concerning victim-offender relationships from recent reports from the FBI. Using the information contained in the tables, you are to develop a preliminary profile of the victim and offender including the probable age, race, and gender of both. To get started, find each of the following using the tables provided.

1. The offender is less than 18
2. The offender is black
3. The offender is male
4. The victim is a white male (Hint: use table 6)
5. The victim is either white or male (Hint: use table 6 and don't forget to to subtract the overlap)
6. The victim and the offender are from the same age category (Include "unknown" as an age category)
7. The victim and the offender are from different age categories (Include "unknown" as an age category) (Hint: use the complement rule)
8. The victim and the offender are of the same race
9. The victim and the offender are of different races (Hint: use the complement rule)
10. The victim and the offender are of the same sex
11. The victim and the offender are of different sexes (Hint: use the complement rule)
12. Without knowing the contents of the forensic team's report, what is your best prediction of the age, race and sex of the victim? Explain your reasoning using probabilities. (Hint: you should be able to use some of the probabilities that you just found to support your prediction. Do NOT just use raw numbers from the tables. Feel free to calculate any additional probabilities that you think would be helpful in supporting your prediction.)
13. What is your best prediction as to the age, race, and sex of the offender? Explain your reasoning using probabilities. (Hint: you should be able to use some of the probabilities that you just found to support your prediction. Do NOT just use raw numbers from the tables. Feel free to calculate any additional probabilities that you think would be helpful in supporting your prediction.)

Part 2 : Soon after you finished this analysis, the preliminary forensics report was delivered to your desk. Although no identification had been made, the autopsy suggested that the cause of death was blunt-force trauma and that the body had been in the water at least 2 weeks. By using a variety of techniques, it was also determined that the victim was a white female with blonde hair. She was estimated as being in her mid-thirties, showed no signs of having had children, and was wearing no jewelry.

Based on this new information, you are to develop a new offender profile by determining the likelihood of the following using the tables provided. Remember, you should now be using conditional probabilities - everything you look up in a table should be based on the information about the victim that you already have.

1. The offender is at least 18
2. The offender is black
3. The offender is male
4. the victim and the offender are from the same age category
5. The victim and the offender are from different age categories (Hint: use complement rule)
6. The victim and the offender are of the same race
7. The victim and the offender are of different races (Hint: use complement rule)
8. The victim and the offender are of the same sex
9. The victim and the offender are of different sexes (Hint: use complement rule)
10. What is your best prediction of the age, race, and sex of the offender? Explain your reasoning using probabilities. (Hint: you should be able to use some of the probabilities that you just found to support your prediction. Do NOT just use raw numbers from the tables. Feel free to calculate any additional probabilities that you think would be helpful in supporting your prediction.)
11. Did your answers to the offender question change once you knew the age, race, and sex of the victim? Explain using the probabilities that you found.

Part 3: It is estimated that 45% of murder victims are known to be related to or acquainted with the offender, that 15% were murdered by an unrelated stranger, and that for 40% of the victims, relationship to their killer is unknown. Based on this and all of the information you found, complete your offender profile for this case. Include explanation of your profile. (This profile report should be completed in paragraph form, using complete sentences.)

HINTS:

1 - For each of the tables provided, compute the totals for each row and column and record them in appropriate boxes. Having these totals done ahead of time will make your work go more smoothly.

2 - Be very careful about which table you are using for each question. Pay attention to the title of the table and the variables being compared. Be especially attentive on the second half when you switch to conditional probabilities.

Victim-Offender Relationship by Age Victim-Offender Relationship by Sex Victim-Offender Relationship by Race Dare of Offender Sex of Victim by Race of Offender Race of Offender Race of Victim by Sex of Offender Sev of Offender Murder Victims by Race and Sex Victim-Offender Relationship by Age Victim-Offender Relationship by Sex Victim-Offender Relationship by Race Dare of Offender Sex of Victim by Race of Offender Race of Offender Race of Victim by Sex of Offender Sev of Offender Murder Victims by Race and Sex