-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.2 summarizes the probabilities of each team winning the game. The optimal mixing rule for the offense is:
A) Randomly pass the ball 3 out of 8 times.
B) Randomly run the ball 5 out of 8 times.
C) Randomly pass the ball 5 out of 8 times.
D) Randomly pass the ball 3 out of 13 times.
E) Randomly run the ball 8 out of 13 times.

Question

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.2 summarizes the probabilities of each team winning the game. The optimal mixing rule for the offense is:
A) Randomly pass the ball 3 out of 8 times. 
B) Randomly run the ball 5 out of 8 times. 
C) Randomly pass the ball 5 out of 8 times. 
D) Randomly pass the ball 3 out of 13 times. 
E) Randomly run the ball 8 out of 13 times.

Quizplus · Accepted Answer

The optimal mixing rule for the offense is to randomly pass the ball 5 out of 8 times. This is because the probability of winning the game is highest when the offense passes the ball 5 out of 8 times.

-Suppose That a Football Team Is Down by 5 Points