Activity Immediate Predecessor Optimistic Time (a) Most Likely Time (b) Pessimistic Time (c) A --- 3 5 8 B --- 2 4 7 C --- 6 8 11 D A, B 5 7 9 E B, C 3 6 10 F C 4 5 6 G E, F 7 10 12 H D 2 3 4 I E, G, H 10 13 16 J G, I, F 12 15 17 K H 8 11 14 Construct a project network. Determine the expected times and variances for each activity. Determine the critical path after you have found ES, EF, LS, LF and Slack. State the path and time the project is expected to take. What is the probability that the project would be completed within 51 days? What is the probability that the project would be completed within 55 days?

Louisiana is busy designing new lottery scratch-off games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: A, B, or C. A can reveal "Loser," "Win $2," or "Win $15." B can reveal "Loser" or "Take a Second Chance." C can reveal "Loser" or "Win $500." On the second chance, the player is instructed to scratch off D or E. D can reveal "Loser" or "Win $2." E can reveal "Loser" or "Win $15." The probabilities at A are 0.70, 0.19, and 0.11. The probabilities at B are 0.75 and 0.25. The probabilities at C are 0.995 and 0.005. The probabilities at D are 0.6 and 0.4. Finally, the probabilities at E are 0.94 and 0.06. Draw the decision tree that represents this scenario. Use proper symbols and label all branches clearly. Calculate the expected value of this game. Choose the correct decision tree below. OA. O C. B Loser (0.995) Win $2 (0.00) Win $500 (0.005) Loser (0.75) 2 Second Chance (0.25) 0 Loser (0.6) 0 Win $2 E Loser (0.70) 0 0.4) 2 Loser (0.94) Win $2…