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) = 0.45 P(B) = 0.55 P(C) = 0.55 P(A and C) = 0.25 P(A and B) = 0.30 P(B and C) = 0.20 P(A and B and C) = 0.15 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 5

This is a continuation of Question 2. You can use the results from Question 2. We are going to draw Venn diagrams in Python using the same setup. Suppose the size of the sample space S is 100. a) [2 points] What is the size of set A? What is size of the set "A and not B"? (You can compute it either in python or by hand. Hints: P(A) = size of A/size of S. To get "A and not B", you may first draw a diagram to assist your understanding.) The following Venn diagrams need to be drawn in Python. By default, set labels using the Big letters (e.g. "A", "B" and "C"). Set title as "Venn diagram for A, B" (or "... for A, C"). The degree of transparency is 0.7. b) [3 points] Draw a Venn diagram for two events A, B. Set colors as (orange, blue). (Hints: use `venn2` and specify `subsets` accordingly. The middle steps to compute the sizes of subsets are optional.) c) [5 points] Draw a Venn diagram for three events A, B, C. Set colors as (orange, blue, red). (Hints: use `venn3` and specify `subsets` accordingly. The middle steps to compute the sizes of subsets are optional.

YOU DONT HAVE TO SOLVE QUESTION TWO, ITS THERE TO HELP YOU WITH QUESTION 5. THANKS