Question

Blue Cab operates 15% of the taxis in a certain city, and Green Cab operates the other 85%. After a night-time hit-and-run accident involving a taxi, an eyewitness said the vehicle was blue. Suppose, though, that under night vision conditions, only 75% of individuals can correctly distinguish between a blue and a green vehicle. What is the probability that the taxi at fault was blue?

Answer 1

0.3462 or 34.62%.

Explanation:

P(B) = 0.15; P(G) = 0.85; P(C)=0.75

The probability that the witness identified a blue car is determined by the probability of the cab being blue and being correctly distinguished by the witness, added to the probability of the cab being green and being incorrectly distinguished by the witness.

`P(W_B) =P(B)*P(C)+P(G)*(1-P(C))\\P(W_B)=0.15*0.75+0.85*0.25\\P(W_B)=0.325`

The probability that a blue car is at fault is given by the probability of a blue car being correctly identified divided by the probability of a blue car being identified by the witness:

`P=(P(B)*P(C))/(P(W_B)) \\P=(0.15*0.75)/(0.325)\\P=0.3462`

The probability is 0.3462 or 34.62%.