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# MAS201 chapter 4 note.pdf MAS 211

Marketplace > University of Miami > Business > MAS 211 > MAS201 chapter 4 note pdf
YALIN ZHANG
UM
Mary McKenry

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Hello, these are the note for chapter 4. I hope it will be helpful for studying the weekly quiz.
COURSE
PROF.
Mary McKenry
TYPE
Class Notes
PAGES
6
WORDS
KARMA
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## Popular in INTRODUCTION TO BUSINESS STATISTICS

This 6 page Class Notes was uploaded by YALIN ZHANG on Sunday February 8, 2015. The Class Notes belongs to MAS 211 at University of Miami taught by Mary McKenry in Winter2015. Since its upload, it has received 283 views. For similar materials see INTRODUCTION TO BUSINESS STATISTICS in Business at University of Miami.

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Date Created: 02/08/15
MAS 201 Chapter 4 Rules of Counting 1 Fundamental Rule of Counting If an experiment with k multiple events can occur such that the first event can occur with n1 possible outcomes and the 53th can ccur with n2 possible outcomes etc then the total number of experim fa omesl 1 2nilt m m mewink Example Coin gram 2 2 1 1 5 6 E Cums Example Pizza mustimam 2 Combinations quoti A combination is the number of possible orderings of N objects f at a time without regard to order 7 is To determine the number of possible outcomes 3 in I 39 l39l 5394 A13 C c 3 cheats 3137 461mm H n Z NN N r Cquot nnNnl 4 C5 3 sue aw AB El AC 39 2 2 25 2 Example Lotto 7 436 439 I L 396 39Ulsf 3 Permutations A permutation is the number of possible orderings of N objects taken n at a time 3m regards to OIEEL A G C 3 I PAN NI lm V39 P g 39 A3 91 EL w mm 32 Example Elections N13 n1 l Mary McKenry 2 f 2 s g 3g 1 Scanned by CamScanner of MAS 201 Chapter 4 Summary De nition of Probability Classical Definition Dice EXampfe Relative Frequency Experiment a Subjective isabel he mutt kmwic g eaglen Axioms of Probability 39 i k are all possible mutually exclusive events then 2 E 1 Rules for Probability la 9 o P A af1 PA weft539 39 Complement CWT 39 PA U B PA 328 PA n B Addition Rule Ian U 3 3 1 Newquot 5 96W 0 U is symbol for Union and is read as or f n 735 8 is symbol for intersection and is read as and 1 it o PAf B PA n B PB Conditional probability 9 i 2 g PA n B PA l B PB Multiplication rule 7 6 Z Does PA n B PA PB Test for independence a PC A If 1 G W o if ys then A and B are independent 7 o if no than A and B are dependentTnot independent it M g a P vcnl 439 if quotIquot y Wm Venn Diagrams 7633 a lacttyoMMi 7 75 Tree Diagrams L I Examples Dice mill rs l t 19 e PUan 1quot w 0 Pan and tasty DE DC Example from text a 0 339 P Eh 39 The following table shows the distribution of blood types in the general population F quot A 3 AB 39 f 0 Pr New 034 009 f 004 g 038 0 Rh e e 006 002 001 if 006 39atlr o i osll 005 039ch What is the probability a person will have type 0 blood a b What is the probability a person will be Rh 0 What is the probability a person will be Rh given she or he has type 0 blood d What is the probability a person will have type B Blood given he or she is Rh a when a pillow l Mary39 MC enry G P B a p y i f gt Sgaellli led by 8ain3canner u a 1 H I Chapter 4 Summary Example from text Suppose that a manager of a large apartment complex provides the following subierctive probability estimates about the number of vacancies that will exist next mon a vacancies Probability 005 015 035 025 010 010 Determine theprobability of the following events a 2QNo vacancies x ou g b At least four vacancies m c LTwo or fewer vacancies 3 0 Sf l l 6b Mr 1 V 19914 quot5quot r L Li Example from text Nd H55 2 i7 I I Data on the 30 largest stock and balanced funds provided 1year and 5year percentage returns for the period ending March 31 1 2000 Suppose we consider a 1eyear return in excess of3950 to be high and a 5year return in excess f 300 to be high 39 a of the funds had 1year returns in excess of 50 of the funds had ear returns in excess of 300 and five of the funds ha 39oth 1 year returns in excess of 50 and 5year returns in excess of 300 w 9 a What is the probability39of a high 1year return 1 06quot 03933 b What is the probability ofahigh5year return d hg a c What is the probability of both a high 1 year return and a high 5year 5 return a t Push 0 Hr 39 30 d What is the probability of neither a high 1 year return nor a high 5y ear return C 39 i C ffth I A higli 5 E C a 7 7 g I jam M545 Hrguc 3 it s i 3 Mary McKenry as g 40 z W 51gt Scanned byCamScanner39 MAS 201 Chapter 4 Summary r 739 a V m Hrig m Bayes Theorem provides a method to apply new information to prior probability in order to obtain posterior revised probabilities 0 Formula PullHg m i B Z PCB I AgtPA f l PBI APA 3 PtB PB APA PB ACPA DU 9 gt 0 I8 0102 16m51 Ac li hc 0 f Nair 7 at If motif pt 1 0401 3 4 7 laxile SC moi nagl V LL 1 Al 0 quotg Di 7 1 1 0 3 il Dcs f 7771 77 I m w 0 Table 7 39 39 k m 1 Events Prior Conditionai Joint 39 Posterior CLWBL W Probability Probability Eff rebaouitkgoba biiity BM f Ai PAi BIAIV l PB nAi RPM I B U Small Car 018 3123 07023 rainy0081203 SW1 Cm o QL no of39 o 4i WWIghp pgn flvl J cit r Example from text PC ra fy Small cars get better gas mileage but they are not as safe as bigger cars Small cars accounted for 18 of the vehicles on the road but accidents involving small cars led to 11898 fatalities during a recent year The probability of an accident involving a small car leading to a fatality is 0128 and the probability of an accident not involving a small car leading to a fatality is 005 Suppose you learn of an accident involving a fatality What is the probability a small car was involved PCJC lkl Pn7lt3amp 30gt 1 Palm 3 028ch 392 0337 Scanned by CamScanner Llqu 39 Magma 1mg mnhvj 111 an exFWWWF39 mmrm an On Mar Sum mi 45 1973 gum 1 amr Liawk n POLLHL Dm h mfj SeamJ 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