Conditional Probability, Independent Events, Odds, and Mathematical Expectation

 

Which is the better bet: - placing a $1 bet on a single number of a Roulette wheel or purchasing a lottery ticket? Because the chance of winning so much money in a lottery is possible, people do not pay attention to the odds. This is the main problem with betting; people often use what they feel is their intuition. With probability, intuition can often be easily deceived.

Assignment Exercises Conditional Probability Independent Events Odds and Mathematical Expectation

Readings Bello & Britton, Sections 10.4-10.6 Probability simulations are found or can be created in almost every math software, Review what probability simulations your school district has.

Web Resources These web resources have links to probability sites.

Assignment

1) The birthday problem, the Monty Hall problem, and the pancake problem, the three mentioned in these material covered this week, are all simulations on the web. Explore one that you might use in your classroom. Post to the discussion forum how you would use it.

Birthday Simulation - http://www.mste.uiuc.edu/reese/birthday/intro.html
Monty Hall Simulation -http://www.shodor.org/interactivate/activities/monty3/index.html
Pancake Simulation - http://www.cut-the-knot.com/pancakes.html

2) Complete the following exercises.

 

Exercises

1) pp. 674-676, Ex. 1, 2, 3, 5, 9, 11, 12, 13, 14, 25, 26, 27

2) pp. 684-686, Ex. 2, 3, 4, 6, 11, 12, 18, 28

3) pp. 695-698, Ex. 1, 2, 3, 4, 5, 6, 7, 26, 34, 37, 44, 45

4) Take this self-checking quiz on probability. at the Math Goodies site: http://www.mathgoodies.com/lessons/vol6/challenge_vol6.html

5) The following three problems are somewhat counterintuitive. Chose one of them:

a) A variation of the birthday problem is the store clerk who marked 24 jars of applesauce at random using a labeling device which can print out any number from 0 to 99. What is the probability that no 2 cans were marked with the same price?

b) A hat check person was angry that no one was leaving him tips. So he decided to distribute the 100 hats to the 100 men at random. What is the probability that nobody was given the correct hat? In 1708, Pierre Rémond de Montmort discovered a formula using factorials for solving this type of problem: Develop this problem for 3 hats and 4 hats and then compare your solution with Montmort's formula.

c) This is a classic problem called the St. Petersburg Paradox. A coin is tossed until a head appears. When a head appears on the first toss, the bank will pay the player $1; when a head appears for the first time on the second toss, the bank will play $2; when a head appears for the first time on the third toss, the bank will pay $4; when a head appears for the first time on the fourth toss, the bank will pay $8; and so forth. How much would you advise some one to pay for playing this game?

Web Resources

A Collection of Conditional Probability Exercises and Solutions!
http://www1.swk.nus.edu.sg/swk/nasri/condprob.html

A Course on Conditional Probability from Stanford University - with links to the Monty Hall simulation
http://www-stat.stanford.edu/~susan/courses/s116/node56.html

Another version of the birthday problem
http://www.cut-the-knot.com/do_you_know/coincidence.html

Independent/Dependent Probability
http://www.learningwave.com/chapters/probability/dependent_independent.html

Interactive Mathematics Probability site - with links to the famous conditional probability problems
http://www.cut-the-knot.com/probability.html

and its full list of Probability Activities under Combinatorics
http://www.cut-the-knot.com/Curriculum/index.html

Lottery Explanations and Problems
http://www.learningwave.com/chapters/probability/prob4.html

Math Goodies Probability Site - independent, dependent and conditional probability
http://www.mathgoodies.com/lessons/toc_vol6.shtm 

Probability Problems and Solutions from Math Forum
http://forum.swarthmore.edu/dr.math/tocs/probability.high.html

Project Interactivate's Gemeralized Monty Hall simulation
http://www.shodor.org/interactivate/activities/monty3/index.html

and the Running Multiple Trials
http://www.shodor.org/interactivate/activities/monty/index.html

Sixth Grade Standards for a school district with probability lesson plans - scroll down the page for probability
http://www.kings.k12.ca.us/math/standards/sixth.html

SMILE PROGRAM MATHEMATICS INDEX - Lesson Plans on Probability
http://www.iit.edu/~smile/mathinde.html#m3

The WWW Tackles the Monty Hall problem - lots of links to the Monty Hall problem with other simulations listed
http://math.rice.edu/~ddonovan/montyurl.html

The Three Door Puzzle- another graphic verison of the Monty Hall simulation
http://www.intergalact.com/threedoor/threedoor.cgi

 

  

Syllabus | Home | Assignments | Bibliography