Probability Concepts Applications

Probability Concepts and Applications

Introduction ,[object Object],[object Object],[object Object]

Basic Statements About Probability ,[object Object],[object Object],[object Object]

Example - continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequencies of Demand

Example - continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Probabilities of Demand

Types of Probability ,[object Object],[object Object],[object Object],[object Object],occurrences or outcomes of number Total occurs event times of Number ) (  event P

Types of Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Mutually Exclusive Events ,[object Object]

Collectively Exhaustive Events ,[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Rolling a die has six possible outcomes

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Rolling two dice results in a total of five spots showing. There are a total of 36 possible outcomes.

Probability : Mutually Exclusive ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Probability: Not Mutually Exclusive ,[object Object],[object Object],[object Object],[object Object],[object Object]

P(A and B) (Venn Diagram) P(A) P(B) P(A and B)

P(A or B) + - = P(A) P(B) P(A and B) P(A or B)

Statistical Dependence ,[object Object],[object Object],[object Object]

Probabilities - Independent Events ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Probability(A|B) Independent Events P(B) P(A) P(A|B) P(B|A)

Statistically Independent Events ,[object Object],[object Object],[object Object],[object Object],A bucket contains 3 black balls, and 7 green balls. We draw a ball from the bucket, replace it, and draw a second ball

Statistically Independent Events - continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Probabilities - Dependent Events ,[object Object],[object Object],[object Object],[object Object]

Probability(A|B) / P(A|B) = P(AB)/P(B) P(AB) P(B) P(A)

Probability(B|A) P(B|A) = P(AB)/P(A) / P(AB) P(B) P(A)

Statistically Dependent Events ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Statistically Dependent Events - Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Joint Probabilities, Dependent Events ,[object Object],[object Object]

Joint Probabilities, Dependent Events - continued ,[object Object],[object Object],[object Object],[object Object],Let M represent the event of the stock market reaching the 10,500 point level, and T represent the event that Tubeless goes up.

Revising Probabilities: Bayes’ Theorem ,[object Object],Prior Probabilities Bayes’ Process Posterior Probabilities New Information

General Form of Bayes’ Theorem

Posterior Probabilities ,[object Object],[object Object],[object Object]

Posterior Probabilities Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Posterior Probabilities Continued ,[object Object],[object Object],[object Object]

Further Probability Revisions ,[object Object],[object Object],[object Object]

Further Probability Revisions - continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Further Probability Revisions - continued

[object Object],[object Object],[object Object],[object Object],[object Object],Further Probability Revisions - continued

Probability Concepts Applications

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