# risk - RISK AND PROBABILITY Uncertainty How can it...

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Uncertainty. How can it be quantified? Should it be included in the decision making process? Risk. Hazard or chance of loss. Examples: Chance of losing money when investing on new IPO’s. Probability. Necessary to analyze risk. When different alternatives might occur, the probability is the proportion of times that one outcome will occur over the long run, if the situation exists repeatedly. If R is the number of repeated occurrences, and if A occurs r times, then P(A)=r/R RISK AND PROBABILITY ChE 4253 - Design I

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Example: Rolling a single die: 1, 2, 3, 4, 5, 6 P (1) = ?, P (6)=? Subjective probability In business, the experiment cannot be repeated many times. Why? Subjective probability is the belief of the decision maker that an event will occur. PROBABILITY ChE 4253 - Design I
Probability distribution. When all possible outcomes are listed and a probability is assigned to each one, a probability distribution is defined. A robot manufacturing company wants to plan their policy. Event Probability of occurrence Develop new robot in 1 year 0.6 New robot is not developed 0.4 1.0 Sum of probability function : 1.0 Event Profit Probability Develop new robot in 1 year \$1,000,000 0.6 New robot is not developed -600,000 0.4 Expected value of profit: 1,000,000*0.6+(-600,000)*0.4=360,000 PROBABILITY AND EXPECTED VALUES ChE 4253 - Design I

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Expected value. The weighted average of the profits corresponding to the various outcomes, each one of these profit figures being weighted by its probability of occurrence. Expected profit π i profit for outcome i N number of possible outcomes P i probability that i will happen PROBABILITY AND EXPECTED VALUES ChE 4253 - Design I ( 29 = = N i i i P E 1 π
Making decisions based on expected profit. Example: Should a tire company raise prices by \$1/tire? Expect \$800,000 profit if successful ad campaign. Expect \$600,000 loss if unsuccessful ad campaign. If 50-50 between successful and unsuccessful, expected profit is 800,000*0.5+(-600,000)*0.5=100,000 What if the company does not raise prices? Suppose certainty of \$200,000 profit. Which option to choose? COMPARISONS OF EXPECTED PROFIT ChE 4253 - Design I

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Visual representation of relevant choices. Decision fork is a juncture where the decision maker chooses. Chance fork is a juncture where “chance” controls outcome. Should our tire company raise prices by \$1/tire? DECISION TREE ChE 4253 - Design I \$200,000 0.5 -\$600,000 0.5 \$800,000 \$100,000 raise Do not raise Successful ad campaign unsuccessful ad campaign
Should OneOK drill a new well? Event Probability of occurrence No oil found 0.6 10,000 barrels found 0.15 20,000 barrels found 0.15 30,000 barrels found 0.1 1.0 If no oil found, loss of \$90,000 If 10,000 bbl, \$100,000 profit If 20,000 bbl, \$300,000 profit If 30,000 bbl, \$500,000 profit DECISION TREE ChE 4253 - Design I

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Should OneOK drill a new well? Assume that maximization of expected profit is pursued.
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## This note was uploaded on 09/07/2009 for the course CBME Kinetics & taught by Professor Lobban during the Spring '09 term at The University of Oklahoma.

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risk - RISK AND PROBABILITY Uncertainty How can it...

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