Question 15.41

9.

Goalie
Left Right
Kicker Goalie’s Left 0.1 0.8
Goalie’s Right 0.8 0.25

9.

The value of the game is , or 0.492. This is achieved by the kicker kicking the ball to the goalie’s left with probability and to the goalie’s right with probability , and by the goalie diving to the left with probability and to the right with probability .