Purchase Behavior for Big-Screen Televisions
|
Planned To Purchase
|
Actually Purchased
|
|
Yes
|
No
|
Total
|
|
Yes
|
200
|
50
|
250
|
|
No
|
100
|
650
|
750
|
|
Total
|
300
|
700
|
1000
|
In the above table, households are classified according to whether they planned to purchase and whether they actually purchased big-screen televisions. Draw the Decision Tree for this example.
Purchase Behavior Regarding Plasma Screen Televisions and DVR.
|
Purchased Plasma Screen
|
Purchased DVR
|
|
Yes
|
No
|
Total
|
|
Plasma Screen
|
38
|
42
|
80
|
|
Not Plasma Screen
|
70
|
150
|
220
|
|
Total
|
108
|
192
|
300
|
- Using the cross-classified data above, construct the decision tree. Use your Decision Tree to find the probability that a household purchased a DVR, given that the household purchased a plasma-screen television.
(Note: the probability formulas for question 2 are listed below)
The probability of A given B is equal to the probability of A and B divided by the probability of B.
P(A/B) = P(A and B)/P(B)
The probability of B given A is equal to the probability of A and B divided by the probability of A.
P(B/A) = P(A and B)/P(A)
Where:
P(A and B) = joint probability of A and B
P(A) = marginal probability of A
P(B) = marginal probability of B