Page 764, Problem 6 updated
Problem Statement:
Pete is considering placing a bet on the NCAA playoff game between Indiana and
Purdue. Without any further information, he believes that each team has an equal chance
to win. If he wins the bet, he will win $10,000; if he loses he will lose $11,000. Before
betting, he may pay Bobby $1,000 for his inside prediction on the game; 60% of the time,
Bobby will predict Indiana will win and 40% of the time, Bobby will predict Purdue will
win. When Bobby says that IU will win, IU has a 70% chance of winning and when
Bobby says that Purdue will win, IU has only a 20% chance of winning.
a) Draw a decision tree and solve it manually.
b) Draw a decision tree and solve it using WinQSB.
Draw a decision tree and solve it manually. By Mr. Abolfazli
PAGE764-PROBLEM#6
-$500
$10000
win$10k(.5)
-$500
lose-$11k(.5)
-$11000
bet on Indiana
-$500
bet on Purdue
win$10k(.5)
$10000
lose-$11k(.5)
-$11000
$2700
win$10k(.7)
$2700
lose -11k(.3)
bet on Indiana
Go for bet
-$5700
$2700
bet on Purdue
Go for bet
$3540
$9000
Do nt bet
$0
perdict of
Indiana winnning
(0.6)
-$12000
win$10k (.3)
lose-$11k(.7)
$3540
$9000
-12000
-$1000
-$7800
$9000
Further
Investigation
-$1000
win$10k(.2)
$4800
perdic of
Purdue winnnig
(0.4)
lose-$11k(.8)
bet on Indiana
$4800
-$12000
$4800
Go for bet
bet on Purdue
win$10k(.8)
lose-$11k(.2)
Do not bet
$9000
-$12000
Do nt bet
-$1000
$0
1
Draw a decision tree and solve it using WinQSB. (Added by Dr. Parisay)
To prepare the decision tree to input into WinQSB, you need to number nodes.
Moreover, you need to define new nodes for terminal points and number them as below:
PAGE764-PROBLEM#6
12: $10000
win$10k(.5)
10
lose-$11k(.5)
13: -$11000
bet on Indiana
9
bet on Purdue
win$10k(.5)
14: $10000
11
lose-$11k(.5)
15: -$11000
win$10k(.7)
16: $9000
6
lose -11k(.3)
bet on Indiana
Go for bet
30
18: $9000
bet on Purdue
Go for bet
Further
Investigation
1
win$10k (.3)
5
3
lose-$11k(.7)
Do nt bet
$0
perdict of
Indiana winnning
(0.6)
17: -$12000
19: -12000
33: -$1000
20: $9000
win$10k(.2)
2
7
lose-$11k(.8)
bet on Indiana
perdic of
Purdue winnnig
(0.4)
21: -$12000
31
Go for bet
bet on Purdue
win$10k(.8)
8
4
Do not bet
lose-$11k(.2)
22: $9000
23: -$12000
Do nt bet
32: -$1000
24: $0
In order to make it easier to input information into the software, I have reduced the
number of nodes to a total of 24 nodes. I selected to eliminate the branches that are not
important for this tree and most probably will not be selected. That is the branches to
nodes 32 and 33. These are “do not bet” decisions that we have one similar to them in
node 24. So the logic will not change much. When eliminating nodes 32 and 33, then we
do not need nodes 30 and 31. Therefore the decision tree will become simplified as
below.
2
PAGE764-PROBLEM#6
12: $10000
win$10k(.5)
10
lose-$11k(.5)
13: -$11000
bet on Indiana
9
bet on Purdue
win$10k(.5)
14: $10000
11
lose-$11k(.5)
15: -$11000
win$10k(.7)
16: $9000
6
lose -11k(.3)
Go for bet
bet on Indiana
3
18: $9000
bet on Purdue
win$10k (.3)
5
perdict of
Indiana winnning
(0.6)
Further
Investigation
1
17: -$12000
lose-$11k(.7)
19: -12000
2
perdic of
Purdue winnnig
(0.4)
20: $9000
win$10k(.2)
7
lose-$11k(.8)
bet on Indiana
21: -$12000
4
bet on Purdue
Do not bet
win$10k(.8)
8
lose-$11k(.2)
22: $9000
23: -$12000
24: $0
3
Input to WinQSB:
4
Output from WinQSB:
5
WinQSB decision Tree:
6