math 30 lecture 5 - PROBABILITY AND STATISTICS COUNTING...

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Unformatted text preview: PROBABILITY AND STATISTICS COUNTING METHODS MATH 30: PROBABILITY AND STATISTICS COUNTING METHODS • is also referred to as COMBINATORICS. • basically concerned with problems of counting as to many ways an event can be done. MATH 30: PROBABILITY AND STATISTICS COUNTING METHODS • Multiplication Rule • Addition Rule • Permutation • Combination MATH 30: PROBABILITY AND STATISTICS MULTIPLICATION RULE If an activity can be constructed in t successive steps and step 1 can be done in 1 ways, step 2 in 2 ways, … and step t can be done in ways, then the number of different possible activities is 1 ∙ 2 ∙ 3 ⋯ ∙ Example: How many ways can we choose a dinner from 5 types of appetizers, 3 types of meat and 4 types of beverages. MATH 30: PROBABILITY AND STATISTICS ADDITION RULE Suppose 1 , 2 , … , are mutually exclusive (or disjoint) sets containing 1 , 2 , … , elements, respectively, then the number of elements that their union contained is the sum of all their cardinalities, i.e., ∪ ∀ = 1 + 2 + ⋯ + Example: In how many ways can one choose a dinner from 5 types of appetizers, 3 types of meat and 4 types of dessert if for chicken, one particular appetizer will not be appropriate while for beef, one particular dessert is not recommended....
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This note was uploaded on 08/30/2011 for the course COMPUTER computer taught by Professor Ms during the Spring '10 term at Oxford University.

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math 30 lecture 5 - PROBABILITY AND STATISTICS COUNTING...

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