v Question Completion Status: QUESTION 4 Given is a Decision Tree Diagram. The P
ID: 329496 • Letter: V
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v Question Completion Status: QUESTION 4 Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below 1/3 Payoff 1 Payo ff 2 Payoff 3 0.3 Pa yo ff 4 0.50 Pa yo ff 5 Alternative A 0.20 Payo ff6 1/3 1/3 Payoff 7 Payoff a Payoff9 Altero ative B 0 30 Payoff 10 0.50 Payoff 11 0.20 Payoff 12 Payoff 13 Payoff 14 1/2 6 1/2 a) The value at node 1 is b) The value at node 3 is c) The value at node 5 is d) The value at node 7 is e) The value at node 8 is f) The best course of action or decision is to select alternative (in 1 decimal place) (in 1 decimal place) (in 1 decimal place) (in 1 decimal place) (in 1 decimal place) QUESTION 5Explanation / Answer
Value = probability of each pay off * respective pay off values ($)
Value at node 1 = 0.3 * {probabilities * pay off values of 1 & 2 & 3}
= 0.3 *{(1/3 *6) + (1/3 * 10) + (1/3 * (-6)}) = 0.3 * {2 + 3.3 – 2} = .99 = 1.0
Value at node 3 = 0.2 * {probabilities * pay off values of 13 & 14}
= 0.2 * {(1/2 * 4) + (1/2 * 7)} = 0.2 *{2 + 3.5} = 1.1
Value at node 5 = 0.3 * {pay off 10 value}
= 0.3 * {8} = 2.4
Value at node 7 = (probabilities * pay off values of 4 & 5 & 6)
= (0.3 * 3) + (0.5 * 8) + (0.2 * 4) = 0.9 + 4 + 0.8 = 5.7
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