Chapter3.1&3.2 lecture notes

Chapter3.1&3.2 lecture notes - Chapter 3.2 Counting...

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AMS 310.01 Class notes September 2, 2003 Chapter 3.1, 3.2 Chapter 3.1 Sample Spaces and Events Basic definitions to be remembered: Experiment -- Example: tossing two fair dice, one red and the other white) Sample space is the set of all possible of outcomes of the experiment. Sample spaces may be finite, discrete and countable, or continuous. Event—subset of the sample space; Example : { the sum of spots on the red and white dice is equal to 7} Events are combined by unions, intersections, and complements. Combinations of events are referred to as compound events. Algebra of set theory Venn diagrams can be used to represent events and compound events. Example : Let {C}denote {ore contains copper} and let {U} denote {ore contains uranium} (1) Represent these two events with Venn diagrams (2) Identify four distinct events which have no intersection as follows: (1) C U (2) C U , (3) C U (4) C U, (3) Identify C U, U C , U C , C U , C and U in terms of 1-4 above and in words.
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Unformatted text preview: Chapter 3.2 Counting Multiplication rule Tree diagrams Theorem 3.1: If sets A 1 , A 2 ,.A k contain, respectively, n 1 , n 2 , n k elements, there are , n 1 n 2 n k-1 n k ways of choosing first an element of A 1 and then an element of A 2 .. and finally an element of A k Example : If a test consists of 12 true-false questions, in how many different ways can a student mark the test paper with one answer to each question? Permutations n r P n n r =-! ( ) ! is the number of permutations of r objects selected from a set of n distinct objects. Example: In how many different ways can one make a first, second, third, and fourth choice among 12 firms leasing construction equipment? Combinations The number of ways in which r objects can be selected from a set of n distinct objects is ( 29 r n n r n r =-! ! ( ) ! . Example: In how many ways can one choose four people for a committee from a total of 8 people? 1...
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