WRoooom is a room detection bot that uses specialized computer vision and temperature sensors to differentiate between Dining room, Bedroom and Bathroom in a house setting. WRoooom senses the presence of a Table and a Rug in these rooms via two special independent computer vision sensors. The prior probabilities of the three rooms are tabulated below.

a. Given the above information, use MAP estimate to detect the room, given that the Table sensor reads True and the Rug sensor reads True.

Choice 1 of 4:Bathroom

Choice 2 of 4:Unable to detect

Choice 3 of 4:Dining Room

Choice 4 of 4:Bedroom

b.

Let A represent the Table sensor reading True, B represent the Rug sensor reading False, and C represent the current robot location being the Dining room. What is P(A, B |C) (the probability of (A and B) given C. )? Round your answer to two decimal places.

The conditional probabilities for each computer vision sensor are tabulated below