6. The Tech football coaching staff has six basic offensive plays it runs every game. Tech has an upcoming game against State on Saturday, and the Tech coaches know that State employs five different defenses. The coaches have estimated the number of yards Tech will gain with each play against each defense, as shown in the following payoff table: Defense Play 54 63 Wide Tackle Nickel Blitz Off tackle 3 -2 7 -1 Option Toss sweep -1 8. 9. 12 6 16 -5 14 Draw -2 4 3 10 -3 Pass 8 20 12 -7 -8 Screen -5 -2 3 16 a. If the coaches employ an offensive game plan, they will use the maximax criterion. What will be their best play? b. If the coaches employ a defensive plan, they will use the maximin criterion. What will be their best play? c. What will be their best offensive play if State is equally likely to use any of its five defenses?
6. The Tech football coaching staff has six basic offensive plays it runs every game. Tech has an upcoming game against State on Saturday, and the Tech coaches know that State employs five different defenses. The coaches have estimated the number of yards Tech will gain with each play against each defense, as shown in the following payoff table: Defense Play 54 63 Wide Tackle Nickel Blitz Off tackle 3 -2 7 -1 Option Toss sweep -1 8. 9. 12 6 16 -5 14 Draw -2 4 3 10 -3 Pass 8 20 12 -7 -8 Screen -5 -2 3 16 a. If the coaches employ an offensive game plan, they will use the maximax criterion. What will be their best play? b. If the coaches employ a defensive plan, they will use the maximin criterion. What will be their best play? c. What will be their best offensive play if State is equally likely to use any of its five defenses?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:6. The Tech football coaching staff has six basic offensive plays it runs every game.
Tech has an upcoming game against State on Saturday, and the Tech coaches know
that State employs five different defenses. The coaches have estimated the number
of yards Tech will gain with each play against each defense, as shown in the following
payoff table:
Defense
Play
54
63
Wide Tackle
Nickel
Blitz
Off tackle
-2
9
7
-1
Option
Toss sweep
-1
-2
12
6.
16
-5
3
14
Draw
-2
4
3
10
--3
Pass
8.
20
12
-7
-8
Screen
-5
-2
3
16
a. If the coaches employ an offensive game plan, they will use the maximax criterion.
What will be their best play?
b. If the coaches employ a defensive plan, they will use the maximin criterion. What
will be their best play?
c. What will be their best offensive play if State is equally likely to use any of its five
defenses?
Transcribed Image Text:12. In Problem 6, the Tech coaches have reviewed game films and have determined
the following probabilities that State will use each of its defenses:
54
Defense
Probability
54
.40
63
.10
Wide tackle
.20
Nickel
.20
Blitz
.10
Using expected value, rank Tech's plays from best to worst.
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