Question

An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positivelong dash that ​is, the probability that the bureau finds a​ match, given that the lead at the crime scene and the lead in the possession of the suspect are actually from two different​ "melts," or sources. To estimate the false positive​ rate, the bureau collected 1 comma 829 bullets that the agency was confident all came from different melts.​ Then, using its established​ criteria, the bureau examined every possible pair of bullets and found 658 matches. Use this information to compute the chance of a false positive. Is this probability small enough for you to have confidence in the​ agency's forensic​ evidence?

Answer 1

Answer / Step-by-step explanation:

In this exercise, we know that the agency collected 1,829 bullets which according to the agency, all came from different source.

The number of pair of bullet is :

         (1,829) = 1, 829 ! / 2! ( 1,829 - 2 ) = 1, 829 x 1,828 x 1827 ! / 2 x 1 x 1,827

          (   2   )

                   = 6, 108,413,724 / 3654

                   = 1671,706.

Also, we know that the agency found 658 matches. According to this, the chance of false positive ( that is, the agencies find a match but the bullets are from two different source ) is

   P (False positive ) = 658 / 671,706

                                   = 0.000979.

The probability is small to an extent, therefore, we should have confidence in the agency forensic report and evidence