PROBABILITY

PROBABILITYProbability is a numerical statement about the likelihood that an event will occur.

Two basic rules regarding mathematics of PROBABILITY:1. The probability of any event or state of nature is greater than or equal to 0 and less than or equal to 1. 0 P 12. The sum of the simple probabilities for all possible outcomes of activity must equal to 1.

Example 1

Quantity demanded (gal)Number of days040180250320410Total 200Quantity demandedPROBABILITY00.20 (40/200)

10.40 (80/200)

20.25 (50/200)

30.10 (20/200)

40.05 (10/200)

Total 1.00 (200/200)TYPES OF PROBABILITY

1. Objective Probability2. Subjective Probability1. Objective Probability- use objective approach. Without performing series of trials, we can often logically determine what the probabilities should be.

P(event) = number of occurrence . total number of occurrence

For example:The probability of tossing a fair coin once and getting a head is?

P(head) = 1 / 2 = 0.50

The probability of drawing a spade out of a deck of 52 playing cards can be logically set as

P(spade) = 13/52 = 0.252. Subjective Probability- based on personal experience , feelings and personal judgments. Use assessment, opinion polls, Delphi method etc.

For example:What is the probability that our economy will be in a severe depression in 2015?

What is the probability that you will become a CPA next year?

Mutually Exclusive and Collectively Exhaustive events

Mutually exclusive if only one of the events cn occur on any one trial .

Collectively exhaustive if the list of outcomes includes every possible outcome. The success or failures that a person experience in life depend on the decisions that he or she makes #SERIOUSTALK

Decision making selecting between two or more alternatives. What makes a good and bad decisions? A good decision is one that is based on logic, considers all available data and possible alternatives and applies the qualitative approach we are about to discuss!Decision theory is an analytical approach to selecting the best alternative or course of action. They depend upon the degree of certainty of the possible outcomes or consequences facing the decision maker.Six steps in decision making1. Define a problem.2. List all alternatives.3. Identify the possible outcomes.4. list the payoffs.5. Select one mathematical decision theory model.6. Apply the model and make decision.3 types of decision models

1. Decision making under certainty2. Decision making under risk3. Decision making under uncertainty1. Decision making under certainty- the decision maker knows with certainty the consequence or outcome of any alternative or decision choice.

For example, You have P1,000 to invest for a one year period. One alternative is to open a savings account that pays 6% another is to invest in a government Treasury bond paying 10%. The treasury bonds will pay a higher return.2. Decision making under risk- the decision maker knows the probability of occurrence of the outcomes or consequences for each choice.

Example:

We may not know whether it will rain tomorrow, but we know that the probability of rain is 30%.3. Decision making under uncertainty- the decision maker does not know the probability of occurrence of the outcomes for each alternative.

For exampleThe probability that a Democrat will be president twenty years from now is not known.DECISION MAKING UNDER UNCERTAINTY

1.Maximax (Optimistic)2. Maximin (Pessimistic)3. Criterion of realism (Hurwicz)4. Equally likey (LaPlace)5. Minimax regret1.Maximax (Optimistic)- is used to find the alternative that maximizes the maximum payoff or consequences.

alternativeF marketUF marketMaximum in a RowConstruct a building200000-180000200000Construct a small building100000-20000100000Do nothing

0002. Maximin (Pessimistic)- used to find alternative that maximizes the minimum payoffs or consequences.

alternativeF marketUF marketMinimum in a RowConstruct a building200000-180000-180000Construct a small building100000-20000-20000Do nothing0003. Criterion of realism (Hurwicz)Compromise between optimistic and pessimistic. Coefficient of realism is selected .

alternativeF marketUF marketHurwiczCOEFF.=0.80Construct a building200000-180000124,000Construct a small building100000-2000076,000Do nothing000124,000= (0.80 x 200,000) + (0.20 x -180,000)4. Equally likey (LaPlace)

Involves finding the alternative with the highest average payoff. Choose the highest average.

alternativeF marketUF marketAverage rowConstruct a building200000-18000010000Construct a small building100000-2000040000Do nothing000Minimax Regret- finds the alternative that minimizes the maximum opportunity loss.alternativeF marketUF marketMaximum in rowConstruct a building0180000180000Construct a small building10000020000100000Do nothing2000000200000Expected Monetary Value- is the weighted sum of possible payoffs for each alternative.

alternativeF marketUF marketEMVConstruct a building200000-18000010000Construct a small building100000-2000040000Do nothing000Probabilities50%50%Expected value of perfect information