Question 2 [13 Points] Let A, B, C be the events corresponding to the following transit...

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Question 2 [13 Points] Let A, B, C be the events corresponding to the following transit options used in the past 30 days: A = car B = bus C = train Suppose the probabilities that a randomly selected Western student used these transit options in the past 30 days are: P(A) = 0.35 P(B) = 0.55 P(C) = 0.40 P(A and C) = 0.10 P(A and B) = 0.20 P(B and C) = 0.15 P(A and B and C) = 0.05 a) [5 points] Sketch a Venn diagram for events A, B, C and the sample space S, and be sure to label the probability of each disjoint subset (the middle calculation steps are optional). b) [1 point] From the Venn diagram, what is the probability that a randomly selected Western student did not use any of these transit options in the past 30 days? (The middle steps are optional.) c) [1 point] From the Venn diagram, what is the probability that a randomly selected Western student used the bus, but no other forms of transit? (The middle steps are optional.) d) [2 points] If a student used the train, what is the probability that this student also used a car? e) [2 points] If a student only used one type of transit, what is the probability that it wasn't the train? f) [2 points] If a student used exactly two types of transit, what is the probability that one of the options was the bus? Question 2 [13 Points] Let A, B, C be the events corresponding to the following transit options used in the past 30 days: A = car B = bus C = train Suppose the probabilities that a randomly selected Western student used these transit options in the past 30 days are: P(A) = 0.35 P(B) = 0.55 P(C) = 0.40 P(A and C) = 0.10 P(A and B) = 0.20 P(B and C) = 0.15 P(A and B and C) = 0.05 a) [5 points] Sketch a Venn diagram for events A, B, C and the sample space S, and be sure to label the probability of each disjoint subset (the middle calculation steps are optional). b) [1 point] From the Venn diagram, what is the probability that a randomly selected Western student did not use any of these transit options in the past 30 days? (The middle steps are optional.) c) [1 point] From the Venn diagram, what is the probability that a randomly selected Western student used the bus, but no other forms of transit? (The middle steps are optional.) d) [2 points] If a student used the train, what is the probability that this student also used a car? e) [2 points] If a student only used one type of transit, what is the probability that it wasn't the train? f) [2 points] If a student used exactly two types of transit, what is the probability that one of the options was the bus?