Probability1. Introduction to Probability2. Applications3. Experiments4. Counting Rules5. Assigning Probabilities
Introduction to ProbabilityProbability : - is a measure of the expectation that an event will occur or a statement is true. Probabilities are given a value between 0 (will not occur) and 1 (will occur). The higher the probability of an event, the more certain we are that the event will occur.
Introduction to Probability Before the middle of the seventeenth century, the term probable (Latin probabilis) meant approvable, andRichard Jeffrey was applied in that sense, univocally, to opinion and to action. A probable action or opinion was one such as sensible people would undertake or hold, in the circumstances
Applications Probability theory is applied ineveryday life in risk assessment and intrade on financial markets. Governmentsapply probabilistic methods inenvironmental regulation
ExperimentsExpriment Exprimental OutcomesToss a coin Win,lose,tieRoll of die Purchase, No purchasePlay a Cricket game Head / tailConduct a sales call 1,2,3,4,5,6
Counting Being able to identify and countthe experimental outcomes is anecessary step in assigning probabilities.Counting Rules.1.Multiple-step experiment’s2.Combinations3.Permutations
Counting1.Multiple-step experiment’s The Multiple – step experiment’s is first counting rule applies to multiple-step Experiment’s
Counting2. CombinationsA second useful counting rule allows one to count thenumber of experiment mental outcomes when theexperiment involves selecting r objects from a (usuallyLarger)Set of n objects. it is called the counting rule forcombinations.
Counting3. Permutations A third counting rule that is sometimes useful is thecounting rule for permutation. It allows one computethe number of experimental outcomes when n objectare to be selected from a set of n object where theorder of selection is important the same r objectsselected in a different order are considered a differentexperimental outcome
Assigning Probabilities Now let us see how probabilities can beassigning to experimenat outcomes. The threeapproaches most frequently1.Classical Method2.Relatvie frequency Method3.Subjective Method
Assigning Probabilities 1.Classical MethodThe Classical Method of Assigning probabilities isappropriate When all the experimental outcome areequally
Assigning Probabilities2.Relatvie frequency Method The Relative frequency Method of assigningprobabilities is appropriate when Data are available toestimate the proportion of the time the experimentaloutcome Will occur if the experiment is repeated a largenumber of time