TABLE 17-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.
$\begin{array}{llcc}
\text {States } &\text { A1 }&\text { A2 }&\text {A3 }\
\hline1&12&-2&8\
2&4&10&5
\end{array}$

$\text {where:}$$\quad $$\quad $ $\text {S1 is state of nature 1 }$$\quad $$\text {A1 is action alternative 1}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\text {S2 is state of nature 2}$$\quad $$\text { A2is action alternative 2}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$ \text {A3 is action alternative3 } $
-Referring to Table 17-1, if the probability of S1 is 0.5, what is the expected opportunity loss (EOL) for A1?
A) 8
B) 7
C) 3
D) 4.5

Question

TABLE 17-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.
 $\begin{array}{llcc}
  \text {States  } &\text { A1 }&\text { A2 }&\text {A3  }\
\hline1&12&-2&8\
2&4&10&5
\end{array}$

$\text {where:}$$\quad $$\quad $ $\text {S1 is state of nature  1 }$$\quad $$\text {A1  is action alternative 1}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\text {S2 is state of nature 2}$$\quad $$\text { A2is action alternative 2}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$ \text {A3 is action alternative3 } $
-Referring to Table 17-1, if the probability of S1 is 0.5, what is the expected opportunity loss (EOL) for A1?
A) 8
B) 7
C) 3
D) 4.5

Quizplus · Accepted Answer

The expected opportunity loss (EOL) for A1 is calculated by first determining the opportunity loss for each state of nature, then multiplying each by the probability of that state, and summing the results. For S1, the opportunity loss is 0 (since A1 has the highest payoff of 12). For S2, the opportunity loss is 6 (since A2 has the highest payoff of 10, and A1 has 4). The EOL for A1 is (0.5 * 0) + (0.5 * 6) = 3.

TABLE 17-1 the Following Payoff Table Shows Profits Associated with a Set

TABLE 17-1
the Following Payoff Table Shows Profits Associated with a Set