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Q1. The route used by a certain motorist in commuting to work contains three intersections with traffic signals. Depending on the traffic lights, she can stop or not stop at the signals. (a) Consider all three signals and describe the sample space for this experiment. (b) Let A be the event of the motorist only stops at the first signal and B be the event of the motorist stops at any of the two lights. Define events A and B. Q2. Each of the possible twelve outcomes of a random experiment is equally likely. The sample space is {a, b, c, d, e, f, g, h, i, j, k,I} . Let A denote the event {b, d, e, h, j}, let B denote the event {c, g, k,1; and let C denote the event (a, e, f, h}. Determine the following: (Three events are shown on the Venn diagram in the following figure. You can work on the diagram - optional) (a) C' ( b) ( An C) U ( An C') (c) (An B) UC (d) (BUA)' (e) (An C)'UB Q3. A certain college team has on its roster three centers, four guards, and four forwards. Students are denoted with letters and some students can play at different positions as follows: Center: X, Y, Z Guard: A, B, X, Y Forward: C, D, E, X a) In how many ways a lineup can be created if X is selected as a center? b) In how many ways a lineup be created if both X and Y are not selected? Q4. Let A denote the event that the next item checked out at a college library is a math book, and let B be the event that the next item checked out is a history book. Suppose that P(A) = 52and P(B) = .28. a. Why is it not the case that P(A) + P(B) = 1? b. Calculate P(Ac) c. Calculate P(A U BC).Q1. The route used by a certain motorist in commuting to work contains three intersections with traffic signals. Depending on the traffic lights, she can stop or not stop at the signals. (a) Consider all three signals and describe the sample space for this experiment. (b) Let A be the event of the motorist only stops at the first signal and B be the event of the motorist stops at any of the two lights. Define events A and B. Q2. Each of the possible twelve outcomes of a random experiment is equally likely. The sample space is {a, b, c, d, e, f, g, h, i, j, k,I} . Let A denote the event {b, d, e, h, j}, let B denote the event {c, g, k,1; and let C denote the event (a, e, f, h}. Determine the following: (Three events are shown on the Venn diagram in the following figure. You can work on the diagram - optional) (a) C' ( b) ( An C) U ( An C') (c) (An B) UC (d) (BUA)' (e) (An C)'UB Q3. A certain college team has on its roster three centers, four guards, and four forwards. Students are denoted with letters and some students can play at different positions as follows: Center: X, Y, Z Guard: A, B, X, Y Forward: C, D, E, X a) In how many ways a lineup can be created if X is selected as a center? b) In how many ways a lineup be created if both X and Y are not selected? Q4. Let A denote the event that the next item checked out at a college library is a math book, and let B be the event that the next item checked out is a history book. Suppose that P(A) = 52and P(B) = .28. a. Why is it not the case that P(A) + P(B) = 1? b. Calculate P(Ac) c. Calculate P(A U BC)