Becoming Certain About Uncertainty

Probability & Statistical Analysis

Math Teacher Leader Seminar

June 2nd & 6th, 2008

Henry Kepner

Kevin McLeod

DeAnn Huinker

Connie Laughlin

Karen Corlyn

Lee Ann Pruske

Paige Richards

Mary Mooney

Session Goals

  • To revisit and deepen our knowledge of probability.
  • To introduce a useful and important representation of sample spaces and probabilities.
  • To describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.
  • To predict the probability of outcomes of simple experiments and test the predictions.

Fair or Unfair?

Game 1

There are 2 chips: one chip with the letter x on both sides. One chip with an x on one side and a y on the other side.

Rules: Flip both chips.

Score: Player I gets a point if there is a match. Player II gets a point if there is no match.

Question: Is this a fair game? Why or why not?

Fair or Unfair Game Prediction Sheet

Directions: Before each game, predict whether the game is fair or unfair and why you feel it is. After each game discussion, clarify your prediction.

Game 1. Fair or Unfair - 2 Chips

Pre-game prediction and justificationPost game thoughts

Game 2. Fair or Unfair - 3 Chips

Pre-game prediction and justificationPost game thoughts

Game 3. Making Purple- Spinners

Pre-game prediction and justificationPost game thoughts


Fair or Unfair?

Game 2

There are 3 chips: one chip with an A on one side and a B on the other side; one chip with an A on one side and a C on the other side; one chip with a Bon one side and a C on the other side.

Rules: Flip all three chips at the same time.

Score: Player I gets a point if any two chips match. Player II gets a point if all three chips are different.

Question: Is this a fair game? Why or why not?


The cost to play the game is $2. The winner gets $6 for making purple. Can the school expect to make money with this game?


Milwaukee Public Schools

Mathematics Framework

Big Ideas

  • Probability is the mathematical expression of likelihood.
  • Probability, expressed as a fraction, will lie between zero and one.
  • Outcomes are not necessarily equally likely.
  • Though individual outcomes cannot be predicted with certainty, patterns emerge over many repetitions.
  • The probabilities of compound events can be computed from the probabilities of the simple events which comprise them.
  • Theoretical models exist which accurately describe the pattern of occurrences of outcomes over many repetitions of a random experiment.

Developed by the Milwaukee Mathematics Partnership (MMP) 1
with support by the National Science Foundation under Grant No. 0314898.1