Try, Try Again

Statistics and Probability

In this poster problem, students get experience with both theoretical and empirical probability for compound events, that is, situations where something happens more than once and they try to find the probability of a particular combination of results.

Materials:

Dice

Learning Objectives:

• List all of the possibilities systematically by finding all the possible combinations of results from two events; this may involve a list, a table, or a diagram such as a tree diagram.
• See that, for example, if there are four equally-likely combinations, each has a (theoretical) probability of 1/4.
• Simulate a phenomenon using dice, spinners, or whatever; record the results; repeat that process many times; and find an empirical probability from those many results (by dividing).
• Distinguish empirical and theoretical results and notice that the more times a trial in conducted, the closer the empirical results will get to the theoretical.

Common Core State Standards for Mathematics:

Note: A probability is a number between zero and one (inclusive), so you can represent it as a fraction, a decimal, or a percent. Which should students use? At this stage, it really doesn’t matter.

But consider the following... For theoretical probabilities using dice, fractions are exact while the others are approximations. If a student always says that the probability of rolling a three is “point one six seven,” they might be missing the elegance of “one sixth.”

If students use fractions, they may have developed the reflex that they have to express every answer in lowest form. Not true! When they do two-dice sums, for example, the probability of rolling a 5 is 4/36. This is better than 1/9 because it contains useful information: there are four ways to get a five among the 36 possibilities.

For empirical probabilities—which are approximations by nature—decimals and percents make it easier to compare.

The Lesson Plan:

Lesson Plan

Slides

Handouts

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Strategic Education Research Partnership
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Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation