1. Analyzing Probabilities and Decisions
Section 4.10

2. Objectives Look at known probabilities and analyze.
Determine the best decision.

3. Example; Analyze Decisions
During a football game, teams have a choice of kicking a short field goal or trying to score on the endzone. Two points are awarded for the field goal and getting the ball into the endzone is worth 4 points.
Probabilities of the 3 Strategies are:
Field Goal Success (2 points) = 60%
Conversion by Running = 57%
Conversion by Passing = 74.3%
If the team gets 12 chances to score this season, which strategy would result in statistically the most points?

4. Example–Solution Field Goal Success… P(Success) = 60% = .6
Expected # of Success = 12(.6)
= 7 Successes
Expected # of Points = 7(2)
= 14 points
Therefore, kicking a field goal every time would give a team 14 points.

5. Example–Solution Conversion by Running Success… P(Success) = 57% = .57
Expected # of Success = 12(.57)
= 7 Successes
Expected # of Points = 7(4)
= 28 points
Therefore, attempting a conversion by running every time would give a team 28 points.

6. Example–Solution Conversion by Passing Success…
P(Success) = 74.3% = .743
Expected # of Success = 12(.743)
= 9 Successes
Expected # of Points = 9(4)
= 36 points
Therefore, attempting a conversion by passing every time would give a team 36 points.
Passing would be the best option because it yields the most points and has the highest probability of success.

7. Example; Analyze Decisions
A laptop company finds a major defect in their laptops which results in their software not working properly during operation. The company must make a decision entirely based on the most cost effective method of fixing this problem. The total laptops sold by the company are 35,560. They could…
a) Recall all laptops:
Fixing cost $350 per laptop
Contacting customer cost $25 per customer
$240,000 fine by government for issuing a recall.
73.2% of customers have laptop serviced on recall

8. Example; Analyze Decisions
b) Defend company against lawsuits:
37.6% are part of plaintiffs
Legal Fees are $56,000 (to keep lawyer on retainer)
$685 awarded per plaintiff.
Average cost of legal fees of $78 per plaintiff. (required)
Which strategy would be a better expected outcome?

9. Example–Solution = $10,239,500 a) Recall all Laptops… Total Cost Cost
To Fix
Cost to
Contact
Cost of
Fine = + +
Cost to Fix = Total Number x $963
Total Number = 35,560(.732)
= 26,030
Cost to Fix = 26,030 x $350
= $9,110,500
Cost to Contact = Total Number x $25
Cost to Contact = 35,560 x $25
= $889,000
Total
Cost =
9,110,500 +
889,000 +
240,000
= $10,239,500

10. Example–Solution
a) Settle Lawsuits…
Total
Cost
Cost of
Plaintiff
Legal
Fees = +
Cost of Plaintiff= # of Plaintiffs x (Legal Fees + Award)
# of Plaintiffs = 35,560(.376)
= 13,370.56
Cost of Plaintiff = 13, x ($78 + $685)
= $10,201,737.28
Total
Cost =
10,201,737.28 +
56,000
= $10,257,737.28
Therefore, it would be cheaper to recall the computer and fix the ones that are sent back.

11. Example; Analyze Decisions
A team has a choice of hitting a short field goal, running for a touchdown, or passing for a touchdown. Three points are given for the field goal, and 6 points for a touchdown.
Probabilities of the 3 Strategies are:
Field Goal Success (2 points) = 75.6%
Conversion by Running = 63.4%
Conversion by Passing = 60%
If the team gets 15 chances to score this season, which strategy would result in statistically the most points?

12. Example–Solution Field Goal Success… P(Success) = 75.6% = .756
Expected # of Success = 15(.756)
= Successes
Expected # of Points = 11.34(3)
= points
Therefore, kicking a field goal every time would give a team about 34 points.

13. Example–Solution Conversion by Running Success…
P(Success) = 63.4% = .634
Expected # of Success = 15(.634)
= 9.51 Successes
Expected # of Points = 9.51(6)
= points
Therefore, attempting a touchdown by running every time would give a team about 57 points.

14. Example–Solution Conversion by Passing Success… P(Success) = 60% = .6
Expected # of Success = 15(.6)
= 9 Successes
Expected # of Points = 9(6)
= 54 points
Therefore, attempting a touchdown by passing every time would give a team 54 points.
Running for a touchdown would be the best option because it yields the most points.

15. 4.10 Analyzing Probabilities and Decisions
Summarize Notes
Read section 4.10
Homework
Worksheet