935270549 (1).ppt - Basic Probability Sanjay Rastogi IIFT 1...

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Sanjay Rastogi, IIFT, New Delhi 1 Basic Probability
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Sanjay Rastogi, IIFT, New Delhi 2 Important Terms Probability – the chance that an uncertain event will occur (always between 0 and 1) Event – Each possible outcome of a variable Sample Space – the collection of all possible events
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Sanjay Rastogi, IIFT, New Delhi 3 Classical Probability Number of outcomes leading to the event divided by the total number of outcomes possible Each outcome is equally likely Determined a priori -- before performing the experiment Applicable to games of chance Objective -- everyone correctly using the method assigns an identical probability P E N Where N e n ( ) : total number of outcomes number of outcomes in E e n
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Sanjay Rastogi, IIFT, New Delhi 4 Relative Frequency Probability Based on historical data Computed after performing the experiment Number of times an event occurred divided by the number of trials Objective -- everyone correctly using the method assigns an identical probability P E N Where N e n ( ) : total number of trials  number of outcomes producing E e n
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Sanjay Rastogi, IIFT, New Delhi 5 Subjective Probability Comes from a person’s intuition or reasoning Subjective -- different individuals may (correctly) assign different numeric probabilities to the same event Degree of belief Useful for unique (single-trial) experiments New product introduction Initial public offering of common stock Site selection decisions Sporting events
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Sanjay Rastogi, IIFT, New Delhi 6 Sample Space The Sample Space is the collection of all possible events e.g. All 6 faces of a die: e.g. All 52 cards of a bridge deck:
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Sanjay Rastogi, IIFT, New Delhi 7 Events Simple event An outcome from a sample space with one characteristic e.g., A red card from a deck of cards Complement of an event A (denoted A’) All outcomes that are not part of event A e.g., All cards that are not diamonds Joint event Involves two or more characteristics simultaneously e.g., An ace that is also red from a deck of cards
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Sanjay Rastogi, IIFT, New Delhi 8 Visualizing Events Contingency Tables Tree Diagrams Red 2 24 26 Black 2 24 26 Total 4 48 52 Ace Not Ace Total Full Deck of 52 Cards Red Card Black Card Not an Ace Ace Ace Not an Ace Sample Space Sample Space 2 24 2 24
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