Class notes

Sta 1000 - Comprehensive notes

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Course
STA1000

Institution
University Of Cape Town (UCT)

This is a comprehensive and detailed note on Introducing probability, Set theory/Probability axioms & theorems/permutations & combinations/ Conditional probability and independence for STA 1000. Quality stuff!! U'll need it!!

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Uploaded on May 18, 2024
Number of pages 5
Written in 2019/2020
Type Class notes
Professor(s) Prof. scott
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sta 1000

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Module 1: Probability: Work Unit 2: Set Theory, Axioms and
Probability
VIDEO OUTLINE

Outcome(s) After watching this video, the student should:

What learning outcomes does • Have a basic understanding of the basic terms and concepts of
this video aim to cover? Set Theory

• Be able to solve some Set Theory problems using Venn
diagrams

Description

What is the video about? The video gives a demonstration of how to tackle some basic set theory
problems. It is assumed the student has already read the material in
Introstat (pp47-52).

• Lecturer confirms that students have read the appropriate material in Introstat so are
familiar with the following terms and concepts:

Today I am going to do some exercises with you demonstrating the use of Venn diagrams.
Before we start, make sure that you have completed your recommended reading in Introstat
and are therefore familiar with the following terms:

• Firstly, lets confirm the correct way to write sets in set notation: The following are
acceptable ways to depict sets:

A = {x | 1 ≤ x ≤ 6}

B = {1;2;3;4;5;6}

C = {integers lying strictly between 0 and 7}

E = {2,4,6}

O = {1,3,5}

Does A=B ? What does this mean?

• Subsets…sets whose elements are all contained in another set. C is a subset of A and of B.
U

(C A) or (A C) (Narrator says: C is a subset of A or A contains C)
U

, • Intersections: the intersection of 2 sets contains those elements common to both (elements
which are in A and in B)

(A∩B) = B

• Empty Set: the set which has no elements (representing an impossible event) ∅

• Mutually Exclusive sets: two sets whose intersection is the empty set are ME. E and O are
ME

• Universal Set and Sample Space. We always depict Venn diagrams as being enclosed in a
rectangular box which represents Sample Space (S) or the set of all possible outcomes.
S

• Unions: The union of sets A and B contains those elements that are either (i) in A or (ii) in B
or (iii) in both A and B. Thus (A U B) contains those elements that are in A or in B (or in both).

• Pairwise Mutually Exclusive and Exhaustive. If we consider an experiment of tossing a six-
sided die then sets D = {1,2} E = {3,4} and F = {5,6} are pairwise mutually exclusive and
exhaustive as together they carve up the Sample space (S) into a partition, with no elements
of S left out.
S

• Complements: the complement of a set contains all those elements that are not in that set

� = 끫롮 = {3,4,5,6}
끫롮 ′

• Examples:

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