Question

During the night there is a hit and run car accident involving a taxi as the perpetrator. There are two taxi companies in this city: the Go Green taxis and the Busy Blue taxis. The Go Green taxis all have green cars and the Busy Blue taxis all have blue cars. A witness on the side-walk identifies the taxi as a blue taxi. A study shows that a person correctly identifies the color of these taxis at night time 85% of the time (i.e., the probability of a person identifying the color as blue when it actually is blue is 0.85, and the probability of a person identifying the color as blue when it is actually green is 0.15). What likelihood ratio do you assign to the witness observations with regard to the following pair of propositions? H_B: The taxi of the hit and run car accident is from the Busy Blue taxi company. H_G: The taxi of the hit and run car accident is from the Go Green taxi company.

Answer 1

HB:

The likelihood ratio that the hit and run car accident is from the Busy Blue taxi company is obtained by taking ratio between the probability of true positive test result and the probability of false positive test result (also known as positive likelihood ratio),

HG:

The likelihood ratio that the hit and run car accident is from the Go Green taxi company is obtained by taking ratio between the probability of false negative test result and the probability of true nrgative test result (also known as negative likelihood ratio),

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