notes and hw

# notes and hw - L A T E X Script Dieter Michael...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L A T E X Script Dieter Michael Schrottshammer Bernhard Ederer Dominik Schlager-Weidinger 4. Oktober 2007 eg ) Tossing a coin twice. S= { HH,HT,TH,TT } A: Tail at the second toss. B: At least one head. A = { HT,TT } , B = { HH,HT,TH } A ∪ B = { HH,HT,TH,TT } = S A ∩ B = { HT } A = { HT,TH } , B = { TT } } ( A ∪ B ) = A ∩ B , ( A ∩ B ) = A ∪ B From the above example, ( A ∪ B ) = Ø = A ∩ B ( A ∩ B ) = { HH,TH,TT } = A ∪ B not a proof } A & B are mutually exclusive (disjoint): If A & B have no outcomes in com- mon. A B S eg ) Tossing a coin twice. A: Tail at the second toss. A = { HT,TT } D: Two heads. D = { HH } A & D are disjoint. 1 2 Counting } Tree Diagrams Example 1: Dinner. Soup: Clam chowder (CC), Broccoli (BR). Vegetable: French Fries (F), Salad (S). Meat: Chicken (C), Beef (B), Pork (P). P B C P B C P B C P B C F F S S CC BR 2 × 2 × 3 = 12 possible choices. } Product Rule Suppose a set consists of ordered collections of k elements. There are n , possible choices for the 1 st element. There are n 2 , possible choices for the 2 nd element. . . . . . . There are n k , possible choices for the k th element. ⇒ There are n 1 · n 2 · ... · n k possible k-tuples. Example 2: 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? 2 · 2 · ... · 2 = 2 12 = 4096 . Definition: Factorial. n ! = n ( n- 1) · ( n- 2) · ... · 2 · 1 1! = 1 0! = 1 } Permutations: Order is important. 2 Definition: An ordered sequence of r objects from a set of n distinct objects: permutation of size r of the objects. n P r = n ( n- 1) · ( n- 2) · ... · ( n- r + 1) = n ! ( n- r )! Example 3: A committee consists of 10 members. #possible choices of the chairman and the vice chair: 10 P 2 = 10! (10- 2)! = 10! 8! = 10 · 9 = 90 } Combinations: Neglect the order....
View Full Document

## This note was uploaded on 03/21/2010 for the course AMS 310 taught by Professor Mendell during the Fall '08 term at SUNY Stony Brook.

### Page1 / 7

notes and hw - L A T E X Script Dieter Michael...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online