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?

Question

Kelton Whitehead

Mathematics

24 May, 06:11

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?

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Answers (1)

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Journey Hunt · 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