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Unformatted text preview: 63 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) 63 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
63 p. 2 ...
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 Spring '11
 Staff
 Addition, Sets, Counting

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