Use the following information to answer Questions The probabilities of obtaining a first down, shown below, are dependent on the choice of the offense and the anticipated choice of the defense. $\begin{array}{lll}
&&&\text { Defense }\
&&\text { Run } &&\text { Pass }\
\text { Offense }&\text { Run } & 0.5 && 0.6 \
&\text { Pass } & 0.8 && 0.4
\end{array}$
-In such situations, what is the optimal solution for the defense?
A) always anticipate a run
B) always anticipate a pass
C) play the mixed strategy $\left( \frac { 2 } { 5 } , \frac { 3 } { 5 } \right)$
D) play the mixed strategy $\left( \frac { 4 } { 5 } , \frac { 1 } { 5 } \right)$

Question

Quizplus · Accepted Answer

The optimal solution for the defense is to play a mixed strategy where they anticipate a run with probability 2/5 and anticipate a pass with probability 3/5. This is because if the defense always anticipates a run, the offense will always choose to pass and have a higher chance of getting a first down. Similarly, if the defense always anticipates a pass, the offense will always choose to run and have a higher chance of getting a first down. By playing a mixed strategy, the defense can prevent the offense from always choosing the option with the higher probability of success.

Use the Following Information to Answer Questions the Probabilities of Obtaining