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# Probability part 4

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### Probability part 4

1. 1. www.mathxtc.comApplicable Mathematics“Probability”
2. 2. DefinitionsProbability is the mathematics of chance.It tells us the relative frequency with which we can expect anevent to occurThe greater the probability the morelikely the event will occur.It can be written as a fraction, decimal, percent, or ratio.
3. 3. DefinitionsCertainImpossible.51050/50Probability is the numerical measureof the likelihood that the event willoccur.Value is between 0 and 1.Sum of the probabilities of all eventsis 1.
4. 4. DefinitionsA probability experiment is an action through which specificresults (counts, measurements, or responses) are obtained.The result of a single trial in a probability experiment is anoutcome.The set of all possible outcomes of a probability experiment is thesample space, denoted as S.e.g. All 6 faces of a die: S = { 1 , 2 , 3 , 4 , 5 , 6 }
5. 5. DefinitionsOther Examples of Sample Spaces may include:ListsTablesGridsVenn DiagramsTree DiagramsMay use a combination of theseWhere appropriate always display your sample space
6. 6. DefinitionsAn event consists of one or more outcomes and is a subset ofthe sample space.Events are often represented by uppercase letters, such as A,B, or C.Notation: The probability that event E will occur is writtenP(E) and is read“the probability of event E.”
7. 7. Definitions• The Probability of an Event, E:Consider a pair of Dice• Each of the Outcomes in the Sample Space are randomand equally likely to occur.e.g. P( ) =(There are 2 ways to get one 6 and the other 4)P(E) =Number of Event OutcomesTotal Number of Possible Outcomes in S181362
8. 8. DefinitionsThere are three types of probability1. Theoretical ProbabilityTheoretical probability is used when each outcome in asample space is equally likely to occur.P(E) =Number of Event OutcomesTotal Number of Possible Outcomes in SThe Ultimate probability formula 
9. 9. DefinitionsThere are three types of probability2. Experimental ProbabilityExperimental probability is based upon observationsobtained from probability experiments.The experimental probability of an eventE is the relative frequency of event EP(E) =Number of Event OccurrencesTotal Number of Observations
10. 10. DefinitionsThere are three types of probability3. Subjective ProbabilitySubjective probability is a probability measure resulting fromintuition, educated guesses, andestimates.Therefore, there is no formula to calculate it.Usually found by consulting an expert.
11. 11. DefinitionsLaw of Large Numbers.As an experiment is repeated over and over, the experimentalprobability of an event approachesthe theoretical probability of the event.The greater the number of trials the more likely theexperimental probability of an event will equal its theoreticalprobability.
12. 12. Complimentary EventsThe complement of event E is the set of all outcomes in asample space that are not included in event E.The complement of event E is denoted byProperties of Probability:EorE)(1)()(1)(1)()(1)(0EPEPEPEPEPEPEP
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