6-3 - 6-3 Basic Counting Principles SET NOTATION A∪B set...

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Unformatted text preview: 6-3 Basic Counting Principles SET NOTATION A∪B set union A∩B set intersection disjoint sets: A∩B = ∅ (empty set) U A' A set complement COUNTING THE NUMBER OF ITEMS IN SETS Notation: n(A) means: the number of items in set A Addition principle: n(A∪B) = n(A) + n(B) – n(A∩B) If A and B are disjoint: n(A∪B) = n(A) + n(B) 6-3 p. 1 COUNTING: THE MULTIPLICATION PRINCIPLE Experiment (2 stages): toss a coin, then throw a die List possible outcomes of: • stage 1: H, T (2 of them) • stage 2: 1, 2, 3, 4, 5, 6 (6 of them) Analysis: • for H on stage 1, there are 6 possibilities for stage 2, giving 6 combined outcomes: H1, H2, H3, H4, H5, H6 • for T on stage 1, there are 6 possibilities for stage 2, giving 6 combined outcomes: T1, T2, T3, T4, T5, T6 • total possible outcomes of the combined experiment? H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 • 12 of them Summary: • for each of 2 outcomes of stage 1, there are 6 outcomes for stage 2 • for a total of 2×6 = 12 combined outcomes Experiment: toss a coin 8 times Total no. outcomes = 2×2×2×2×2×2×2×2 = 28 = 256 The multiplication principle If a process proceeds in several stages each of which has a certain number of outcomes, to compute the total # of outcomes of the combined process: 1. determine the # of outcomes of each stage separately 2. multiply those #’s 6-3 p. 2 ...
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6-3 - 6-3 Basic Counting Principles SET NOTATION A∪B set...

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