A special delivery truck travels from point A to point B and back over the same route

Question:

A special delivery truck travels from point A to point B and back over the same route each day. There are three traffic lights on this route. Let X be the number of red lights the truck encounters on the way to delivery point B and let Y be the number of red lights the truck encounters on the way back to delivery point A. A traffic engineer has determined the joint probability distribution of X and Y shown in the table.

a. Find the marginal probability distribution of Y.
b. Given that the truck encounters X = 2 red lights on the way to delivery point B, find the probability distribution of Y.