Probability Archives - The Nature of Mathematics

Individual Research Projects Section13.1

September 29, 2015July 20, 2015 by elaine

Project 13.1

Devise a fair scheme for eliminating coins in this country.

Here is an alternative question:
Michael Rossides has come up with a scheme for eliminating coins. This scheme involves probability and the fact that most cash registers today … See the whole entry

Video Links 13-4

August 11, 2015July 20, 2015 by elaine

Video:
Independent events; probability of an intersection (time: 8:03)

Tree diagrams (time: 6:07)
… See the whole entry

Video Links 13-3

August 11, 2015July 20, 2015 by elaine

Videos:
Odds and Probability (time: 2:53)

Conditional Probability (time: 11:07)
… See the whole entry

Video Links 13-1

August 11, 2015July 20, 2015 by elaine

Videos:
This is a general introduction to probability. (time: 9:25)

Probability – Part 1 (time: 10:29) This is the first of 8 videos on this topic. If you are interested in this one, click the links at the right on … See the whole entry

Reference Topics 13-6

April 17, 2018July 20, 2015 by elaine

Here is a statement of the binomial theorem (with links):
http://mathworld.wolfram.com/BinomialTheorem.html

This link gives some examples of the binomial theorem:
http://www.purplemath.com/modules/binomial.htm

This site provides a summary of the binomial distribution.
http://www.stat.yale.edu/Courses/1997-98/101/binom.htm

This site calculates the binomial probabilities.
http://stattrek.com/online-calculator/binomial.aspx… See the whole entry

Reference Topics 13-2

May 19, 2024July 20, 2015 by elaine

This site presents an essay on probability and gambling:
http://www.pbs.org/wgbh/pages/frontline/shows/gamble/odds/

You might wish to test the definition of mathematical expectation by actually tossing a coin or rolling one or two dice. These links (from Section 11.1) will simulate many repetitions … See the whole entry

Homework Hints 13-5

May 23, 2024July 20, 2015 by elaine

Problems 1-6
Use the tree diagram to find each requested probability. See Example 1.

Problem 7-12
Use a tree diagram and Bayes’ theorem. See Example 4.

Problem 13-24
Use the Venn diagram and look for the given set. See Example … See the whole entry

Homework Hints 13-4

October 22, 2015July 20, 2015 by elaine

Problem 1
Look in the book to find a statement of this term.

Problems 2-3
Make sure you know these formulas, as well as the conditions for which each applies.

Problem 4
Look in the book to find a statement … See the whole entry

Homework Hints 13-1

May 23, 2024July 20, 2015 by elaine

Problems 1-4
These problems are reviewing the basic ideas of probability. Make sure you can answer each of these questions (even if the problems are not assigned).

Problems 5-8
First, find the proportion of the circle included in each region. … See the whole entry

Section 13.5: Bayes’ Theorem

September 25, 2015July 20, 2015 by elaine

13.5 Outline

Probabilities with a partition of a sample space
1. partition of a set
2. probability of a partitioned event
A posteriori probabilities
1. a priori probabilities
2. a posteriori probabilities
3. Bayes’ theorem

13.5 Essential Ideas

Partition of a set: A set … See the whole entry