Problem 3 The events A and B on probability space (9, .F, P) satisfy lP'(AC n B) = 0.31, IP'(A U B) = 0.79, and IP'(A n B) = 0.25. Evaluate 100 - P(A). Show solution Problem 4 A group of friends plans to visit only these four groups of animals at the zoo: aligators, bees, camels, and dolphins. They are deciding on the order in which the animals should be visited. One of the following schedules will be chosen at random: 0 1. Visit the aligators first, then bees, then camels, and finally dolphins. o 2. Visit the dolphins, then aligators, then camels, then bees. o 3. Visit the camels, then dolphins, then aligators, then bees. - 4. Visit the bees, then aligators, then dolphins, then camels. o 5. Visit the camels, then bees, then aligators, then dolphins. Each of the above five plans has equal chance of being selected. Construct the probability space (9,7,1?) that corresponds to the described random experiment. Determine the set that corresponds to the event that the dolphins are visited before the aligators. Show solution Problem 5 The random variables X and Y are independent. The codomain of both random variables X and Y is the set {10, 11, 12, . . . , 110}. It is known thath'(X = 10): 131,]P'(Y = 11) = 121, and IP'(Y > 11|X > 12): %. What is 242 - 1P(X+ Y = 20)