Instruction 17-3
The following payoff table shows profits associated with a set of three alternatives under two possible events.
$$\begin{array} { c c c c }
\text { States } & A 1 & A 2 & A B \
\hline 1 & 12 & - 2 & 8 \
2 & 4 & 10 & 5
\end{array}$$ where:
S1 is event 1
A1 is action alternative 1
S2 is event 2
A2 is action alternative 2
A3 is action alternative 3
-Referring to Instruction 17-3,if the probability of S1 is 0.5,then the expected opportunity loss (EOL)for A1 is _______.
A) 4.5
B) 3
C) 8
D) 7

Question

Instruction 17-3
The following payoff table shows profits associated with a set of three alternatives under two possible events.
 $$\begin{array} { c c c c } 
\text { States } & A 1 & A 2 & A B \
\hline 1 & 12 & - 2 & 8 \
2 & 4 & 10 & 5
\end{array}$$ where:
S1 is event 1
A1 is action alternative 1
S2 is event 2
A2 is action alternative 2
A3 is action alternative 3
-Referring to Instruction 17-3,if the probability of S1 is 0.5,then the expected opportunity loss (EOL)for A1 is  _______.
A) 4.5
B) 3
C) 8
D) 7

Quizplus · Accepted Answer

To find the EOL for A1, we need to calculate the sum of the products of the probabilities and the opportunity losses for each action alternative, and then subtract the result from the maximum payoff. 
Maximum payoff for A1 = 18
EOL for A1 = (0.5 x 2) + (0.5 x 7) = 4.5 
Thus, the expected payoff for A1 is 18 - 4.5 = 13.5. 
Similarly, the expected opportunity loss for A2 is (0.5 x 1) + (0.5 x 4) = 2.5 and for A3 is (0.5 x 4) + (0.5 x 3) = 3.5.
Therefore, A1 has the highest expected payoff, and is the best choice.

Instruction 17-3 the Following Payoff Table Shows Profits Associated with a Set

Instruction 17-3
the Following Payoff Table Shows Profits Associated with a Set