Robot is in the world with 3 locations A B C The probability

Robot is in the world with 3 locations A, B, C.

The probability that the Robot is in one of location is: P (A) = P(B) = P(C ) = 1/3.

The color of location A is Red while the colors of location B and C are Green.

Robot has a sensor to detect a color, but the sensor is unreliable. The probability that it senses the color of location correct is only 0.9 for each location.

P(Red | A) = P(Green | B) = P(Green | C) = 0.9

Robot is seeing Red currently.

[1] What is the probability that the Robot is in location A?  

[2]   What is the probability that it is in location B?

[3]   What is the probability that the Robot is in C?

Solution