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 the delivery point A. A traffic engineer has determined the joint probability distribution of X and Y shown in the table: X = x
Y = y 0 1 2 3
0 0.01 0.02 0.07 0.01
1 0.03 0.06 0.1 0.06
2 0.05 0.12 0.15 0.08
3 0.02 0.09 0.08 0.05
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.