It is cold in Michigan and you are dreaming of taking a vacation to the beaches of the Bahamas. You decide to look up airlines because you are curious what prices are these days. You find a new airline that has some interesting rules about emotional support animals. While you are aware that many airlines allow dogs, you find that this company has allowed peacocks on flights, as well as goldfish. You are now curious what the probability is of having passengers on a flight that have different animals with them. You reach out to the company and find out the following probabilities: For notation, we simplify peacock as the set p, goldfish as the set G, and dog as the set D P(p) = 0.1 P(G) = 0.1 P(D) = 0.6 P(p nD) = 0.02 P(G n D) = 0.05 P(p n G) = 0.01 P(p n D n G) = 0.005 a) [14 pts] Fill out the Venn Diagram with the probabilities of each region. Label each region with the set notation describing that region. Show your work on how you found each region's probability. b) [2 pts] What is the probability that there will be a peacock, but no goldfish on the flight? Express the statement in set notation and calculate the associated probability. c) [2 pts] What is the probability that there will be exactly two of the three animals (peacock, goldfish, dog) on a flight? Express the statement in set notation, and calculate the associated probability