MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES
MTH 245

Spring 2014
Sec. 6.1 Experiments, Outcomes= Sample Spaces and Events
Many events in our lives appear to be random.
But repeated observations over time Show that there are longterm patterns
that are present in spite of short term ﬂuctuations.
Probability is the study
MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES
MTH 245

Spring 2014
5,3 VENN DIAGRAMS AND COU/UT/NG.
A VE'NN DIAGRAM FOR Two
SETS Din/logs u INTO Foal? BASIC,
REGIONS
A VENN DIAGRAM FOR THREE
SETS K, s, and. T When using VQW diagrams To CounT
if” is offem USeful To Wrife M tXAMFLE A TOTAL. OF 797 NOBEL
Panes HAD BEEN
MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES
MTH 245

Spring 2014
EXAMPLE FROM LAST TIME DE MORGAN‘S LAWS WON FOR 3 OR MORE
SETS AS WELL
/
(AﬂBnC) '= A’UBIUC’
(A U B uC)’ '‘ A’nB’nC/
/
(Aug/UC/) = 59» A‘Funcfctmeufa/ PPMH/o/e of Coo175x,
H A is Cg SalL
é”
h(A3 Aenores ”IQ deer of debug«(‘5
in A
WhaT 1'5 & FormU/Q
MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES
MTH 245

Spring 2014
Sec. 5.5 + 5.6
Permutations and Combinations and Further Counting Problems
Def: A subset of distinct elements selected from a
single given set and arranged in a specic order is
called a permutation.
Properties:
a) Once an element is selected, it cannot be
MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES
MTH 245

Spring 2014
Sec 5.1 Sets
A set is a collection of objects, called elements.
A set is well deﬁned When there is no ambiguity as to the objects
(elements) that make up the set.
Notation: A = { Fred, Ahmed, Maria }
The set A is a collection of the names: Fred, Ahmed and