Question: 1 a body was recovered from a drainage ditch and...
1.) A body was recovered from a drainage ditch and brought to the county’s Office of the Medical Examiner. Upon examination of the body, the pathologists discovered that the deceased had a hip replacement, and they were able to read the brand (Hipster Manufacturing) and serial number (167482828) for the metal hip socket. The case investigator contacted the company to see if they could tell him anything further about the particular serial number. Hipster Manufacturing stated that the serial number represented a batch of 100 hip replacement parts that were distributed throughout the U.S. at random, each with this same serial number on it. By looking up additional statistics on all hip replacement companies servicing the U.S., the investigator found that at present there are 89,000 hip replacement parts. Therefore, the frequency of the particular part found in the body is 1 of the 100 out of 89,000 present in the U.S., and can be calculated at 100/89,000.
Therefore, the probability of having serial #167482828 = P(serial # 167482828) = ?
Upon further investigation, the investigators noticed that the individual had traces of soil embedded under his fingernails. This soil was identified as bentonite. About 5% of the U.S. population lives in areas where this type of clay is found.
A missing persons report file for T.W. Dwight came up, and he had undergone hip surgery several years ago and happened to live in an area that had bentonite in the soil. When Dwight's physician was contacted and asked about the serial number documented in Dwight's medical records for his hip replacement, the serial number matched that found in the John Doe.
What is the probability for both the serial number and the bentonite to be found in combination? (Assume these 2 events are independent.)
How probable is it that the John Doe and T.W. Dwight are the same person?