Question

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens. All taxis in Athens are blue or green. You swear, under oath, that the taxi was blue. Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable (i.e., if the taxi was green, it appears green to you 75% of the time, and blue otherwise; similarly, if the taxi was blue, it appears blue to you 75% of the time, and green otherwise).

Required:
a. Is it possible to calculate the most likely color for the taxi? (Hint: distinguish carefully between the proposition that the taxi is blue and the proposition that it appears blue.)
b. What if you know that 9 out of 10 Athenian taxis are green?

Answer 1

A ) Yes it is possible

B) The color of the most likely taxi to hit the victim is Green in color because

P( Tg / Yb ) = 0.75 = 75%

Explanation:

A) Yes it is possible

attached below is a proposition that can be used to calculate the most likely color of the taxi

where: Tg = taxi is green

Tb = Taxi is blue

Yg = green taxi is seen

Yb = blue taxi is seen

B) When 9 out of 10 Athenian taxis are green

The color of the most likely taxi to hit the victim is Green in color because

P( Tg / Yb ) = 0.75 = 75%