Analyzing Probabilities and Decisions Skill 22

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

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?

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.

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.

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.

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

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?

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

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 = 13,370.56 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.

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?

Example–Solution Field Goal Success… P(Success) = 75.6% = .756 Expected # of Success = 15(.756) = 11.34 Successes Expected # of Points = 11.34(3) = 34.02 points Therefore, kicking a field goal every time would give a team about 34 points.

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) = 57.06 points Therefore, attempting a touchdown by running every time would give a team about 57 points.

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.

22: Analyzing Probabilities and Decisions Summarize Notes Questions? Homework Worksheet