Question

After a robbery, a thief jumps into a taxi and disappears. An eyewitness on the crime scene is telling the police that the cab is yellow. In order to make sure that this testimony is worth something, the assistant district attorney makes a Bayesian analysis of the situation. After some research, he comes up with the following information: (1) In that particular city, 80% of taxis are black and 20% of taxis are yellow; and (2) Eyewitnesses are not always reliable and from past experience, it is expected that an eyewitness is 80% accurate. In other words, he will identify the color of a taxi accurately (yellow or black) eight out of ten times. What is the probability that the cab was really yellow, given that it was reported as being yellow

Answer 1

The probability that the cab was really yellow given that it was reported as being yellow is 0.32.

Given that there are 80% black taxis and 20% yellow taxis, witness is 80% accurate.

Probability is the chance of happening an event among all the events possible. It lies between 0 and 1. The value of probability can be calculated through the following formula:

Probability=Number of items/ total items.

Black taxis=80%

Yellow taxs=20%

Eyewitness is accurate=80%

Probability that the cab was really yellow=

P(X=Yellow)P(Witness is correct)+P(X=Black)P(Witness is incorrect)

Probability that car is black=0.8

Probability that car is yellow=0.2

Probability that witness is correct=0.8

Probability that witness is incorrect=1-0.8

=0.2

We have to just put the values in the formula given above.

Required probability=0.2*0.8+0.8*0.2

=0.16+0.16

=0.32

Hence the probability that the cab is really yellow is 0.32.

Learn more about probability at https://brainly.com/question/24756209

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