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?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

See similar textbooks