A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinations of colors is given in the following
table:
Second light

First Light R Y G

R 0.30 0.04 0.16
Y 0.05 0.01 0.04
G 0.15 0.05 0.20
a. What is the probability the first light is red?
b. What is the probability that the second light is green?
c. Find the probability that both lights are the same color.
d. Given that the first light is red, find the probability that the second light is green.
e. Given that the second light is yellow, find the probability that the first light was red.