Blue cab operates 15% of the taxis in a certain city, and green cab operates the other 85%. after a nighttime hit-and-run accident involving a taxi, an eyewitness said the vehicle was blue. suppose, though, that under night vision conditions, only 80% of individuals can correctly distinguish between a blue and a green vehicle. what is the (posterior) probability that the taxi at fault was blue?

The required probability is 0.414.

Step-by-step explanation:

Since we have given that

Probability of taxis in a certain city by Blue Cab P(B)= 15%

Probability of taxis by Green Cab P(G) = 85%

Let A be the event that eyewitness said that vehicle was blue.

P(A|B)=0.80

P(A|G)=0.80

P(A'|B)=0.20=P(A'|G)

Using the "Bayes theorem":

Probability that the taxi at fault was blue is given by

Hence, the required probability is 0.414.

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