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Chapter 1.1-1.2

STAT 305 Chapter Notes - Chapter 1.1-1.2: Sample Space

Department
Statistics
Course Code
STAT 305
Professor
Roy
Chapter
1.1-1.2

This preview shows half of the first page. to view the full 2 pages of the document. 1.1
Sample space of an experiment is all of its possible outcomes
The simplest is a binary outcome as there are 2 possible outcomes
Sample space denoted as S = {N, D} where N represents not defective, and D
represents defective
Gender of baby in a hospital: S= {M, F}
An event is any collection of outcomes
Simple if it has one outcome, compound if it has more than one outcome
Complements to an event are the set of outcomes not contained in the event
Some events will intersect
ie) “A ∩ B” means “A and B” is the event consisting of all outcomes that are in
both A and B
Events can also be in union
ie) “A U B” means A or B and is events consisting all outcomes A or B
De Morgan’s Law says if A and B are 2 events in sample space of some experiment,
then (A U B) = A’ ∩ B’ and (A ∩ B) = A’ U B’
When there are no outcomes in common, it is said the events are disjointed
1.2
The sum of the probabilities of each of the independent outcomes in an event add up to
1
There must be a distinction between the long term probability and the short term
likelihood
The long term probability of a dishwasher needing warranty service being 10%
does not mean that 1 out of every 10 dishwashers will need this service
Addition rule says P(A U B) = P(A) + P(B) - P(A ∩ B)
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