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3. Bayesian Inference A cab was involved at night in a hit and run accident. In this town there are only two cab companies, the Blue with 80% of the cabs and the Green company with the remaining 20%. As it happened there was a witness to the accident who identified the hit and run cab as Blue. The case came to trial. An important part of the testimony was a test of the reliability of the eyewitness to identify a cab as being either Blue or Green under the same circumstances as those that existed the night of the accident. The result of these tests was that the witness correctly identified a blue cab as blue 70% of the time and a green cab as green 80% of the time. On the basis of the claim of the eyewitness and the test conducted by the court, what is the probability that the cab involved in the accident was in fact Blue as the witness had claimed?

3. Bayesian Inference A cab was involved at night in a hit and run accident. In this town there are only two cab companies, the Blue with 80% of the cabs and the Green company with the remaining 20%. As it happened there was a witness to the accident who identified the hit and run cab as Blue. The case came to trial. An important part of the testimony was a test of the reliability of the eyewitness to identify a cab as being either Blue or Green under the same circumstances as those that existed the night of the accident. The result of these tests was that the witness correctly identified a blue cab as blue 70% of the time and a green cab as green 80% of the time. On the basis of the claim of the eyewitness and the test conducted by the court, what is the probability that the cab involved in the accident was in fact Blue as the witness had claimed?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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3. Bayesian Inference A cab was involved at night in a hit and run accident. In this town there are only two cab companies, the Blue with 80% of the cabs and the Green company with the remaining 20%. As it happened there was a witness to the accident who identified the hit and run cab as Blue. The case came to trial. An important part of the testimony was a test of the reliability of the eyewitness to identify a cab as being either Blue or Green under the same circumstances as those that existed the night of the accident. The result of these tests was that the witness correctly identified a blue cab as blue 70% of the time and a green cab as green 80% of the time. On the basis of the claim of the eyewitness and the test conducted by the court, what is the probability that the cab involved in the accident was in fact Blue as the witness had claimed?
Transcribed Image Text:3. Bayesian Inference A cab was involved at night in a hit and run accident. In this town there are only two cab companies, the Blue with 80% of the cabs and the Green company with the remaining 20%. As it happened there was a witness to the accident who identified the hit and run cab as Blue. The case came to trial. An important part of the testimony was a test of the reliability of the eyewitness to identify a cab as being either Blue or Green under the same circumstances as those that existed the night of the accident. The result of these tests was that the witness correctly identified a blue cab as blue 70% of the time and a green cab as green 80% of the time. On the basis of the claim of the eyewitness and the test conducted by the court, what is the probability that the cab involved in the accident was in fact Blue as the witness had claimed?
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