What Are My Chances

This is URL provides an activity that instructs students to conduct five experiments through stations to compare theoretical and experimental probability. Hands- on activity that allows students to rotate to different stations. Students find probability, build ratios and convert ratios to decimals and fractions.

Weblink address (URL): 
Probability Exploration

Standards & Objectives

Learning objectives: 

Students will:

  • Use probabilities to predict trends.
  • Interpret the relationship between experimental and theoretical probabilities.
  • Explore the Law of Large Numbers.
Essential and guiding questions: 
  • Is there a connection between theoretical and experimental probability?
  • How could you explain the two type of probability to someone who hasnever heard of them?
  • Why is it useful to know about probabilities?

Lesson Variations

Blooms taxonomy level: 
Applying
Extension suggestions: 
  • Ask students to make a prediction table as to what they think the results will be through 30 trials of a coin toss. Have them number 1 through 30 on a piece of paper and record H or T for what they think will come up for each trial. Most students will end with experimental probabilities around 1/2 and will not put 6 or 7 heads in a row through the table, even though it is possible that the coin will land heads up for 7 in a row. Then, have students run 30-trial experiments and compare their predictions to actual trials. Discuss the word random and what it really means. Key question: If 7 heads come up in a row, does that mean tails is due?
  • Introduce students to the Monte Carlo problem.
  • Introduce the term equally likely events to students. Give them the example of tossing a die. The chances of rolling evens or odds are equally likely. Both have a 50% chance of happening. The probability of rolling a number less than 2, equal to 2, or greater than 2 are not equally likely. Rolling a number greater than 2 is much more likely. Read a list of events to students and have them respond whether each has equally likely outcomes. You could also have them place pennies on a scale between 0 and 100% where they think each of the probabilities will be. If the coins are in the same spot, the outcomes are equally likely. For example if you ask the chance of it raining today, students should place one coin to represent the chance of it raining and another to represent the chance of it not raining. If both coins are on 50%, then the events are equally likely. You may also need to discuss with students that the probabilities have to add up to 100%.
  • Move on to the next lesson, Probably Graphing.

Helpful Hints

Materials:

  • Dice
  • Pennies or other coins
  • Several decks of Cards
  • Calculators
  • What Are My Chances? Activity Sheet 
  • Computers or tablets with internet connection (optional)

References

Contributors: 
Leslie Wolfe
Originator: 
Ayers Institute for Learning & Innovation