Here, we consider one of the simplest models of a random experiment with m possible outcomes. We assume (believe) that these outcomes are equally likely, so the probability of an event consisting of n outcomes is simply m In the framework of general probability spaces, this means that we assume that is a finite set (with m elements), Σ = 2, and P({w}) = for each WEN; hence, m P(A): = #A #52° We shall call such probability spaces classical and refer to P as the uniform probability measure. It is useful to know some formulas for computing the numbers of elements of various finite sets. 2.1 What is the number of subsets of an n-element set? 2.2 2.3 2.4 In how many ways can you order an n-element set? What is the number of all k-element subsets of an n-element set? What is the number of all one-to-one mappings from an n-element set to an m-element set?
Here, we consider one of the simplest models of a random experiment with m possible outcomes. We assume (believe) that these outcomes are equally likely, so the probability of an event consisting of n outcomes is simply m In the framework of general probability spaces, this means that we assume that is a finite set (with m elements), Σ = 2, and P({w}) = for each WEN; hence, m P(A): = #A #52° We shall call such probability spaces classical and refer to P as the uniform probability measure. It is useful to know some formulas for computing the numbers of elements of various finite sets. 2.1 What is the number of subsets of an n-element set? 2.2 2.3 2.4 In how many ways can you order an n-element set? What is the number of all k-element subsets of an n-element set? What is the number of all one-to-one mappings from an n-element set to an m-element set?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Here, we consider one of the simplest models of a random experiment with
m possible outcomes. We assume (believe) that these outcomes are equally
likely, so the probability of an event consisting of n outcomes is simply
In the framework of general probability spaces, this means that we assume
that N is a finite set (with m elements), E = 2", and P({w}) = for each
WE N; hence,
m
#A
P(A):
We shall call such probability spaces classical and refer to P as the uniform
probability measure.
It is useful to know some formulas for computing the numbers of elements
of various finite sets.
2.1
What is the number of subsets of an n-element set?
2.2
In how many ways can you order an n-element set?
2.3
What is the number of all k-element subsets of an n-element set?
2.4
What is the number of all one-to-one mappings from an n-element
set to an m-element set?
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VIEWStep 4: 2.3)Determine the number of all k element subsets of an n element set
VIEWStep 5: 2.4)Determine the number of all one-to-one mappings from an n-element set to an m-element set
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