Understanding Probability

In this lesson, students learn what probability is, learn different way to express probability numerically, and learn how to solve problems based on probability. This lesson plan calls for a particular video but it is not necessary.

Standards & Objectives

Academic standards
GLE 0606.5.1
Understand the meaning of probability and how it is expressed.
SPI 0606.5.1
Determine the theoretical probability of simple and compound events in familiar contexts.
 
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Learning objectives: 

Students will:

  • learn what probability is
  • learn different ways to express probability numerically: as a ratio, a decimal, and a percentage
  • learn how to solve problems based on probability.
Essential and guiding questions: 

Discussion Questions:

  • Name professions that use probability. Give an example. Many scientists and social scientists use probability, including epidemiologists, psychologists, economists, and statisticians. They predict outcomes of events, such as the incidence of diseases and the strength of the stock market.
  • Imagine you are on the school debate team and the subject at hand is whether companies should drill for oil in Antarctica. What statistics would you look for if you're arguing in favor of oil exploration there? What statistics would you look for to support your argument against drilling there? What are some ways that numbers could support arguments on both sides?
  • Think about numbers you may have seen in advertisements, such as "X Juice is 90 percent real juice," or "Y cereal has 35 percent of the total vitamins needed in one day." How would you write each percentage as a ratio?
  • What does it mean when you hear the weather reporter predict a 10 percent chance of rain? Is that a high or low probability?
  • Express the probability that your mother will let you have a sleepover next weekend as a probability, assuming that the total number of outcomes is 100. What factors would increase the probability that she would say yes? (If you finish all your homework and chores, go to bed on time.) What factors would decrease the probability that she would say yes? (If you misbehave, do not finish your homework or chores, or go to bed on time.)
  • How do you think authors of The Farmer's Almanac make their predictions about weather for a year? How do you think they use probability?

Lesson Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

Adaptations:

Work on the Classroom Activity Sheet as a whole-class activity. Have students write their answers as a ratio only. Then challenge students to work on the Take-Home Activity Sheet in pairs. Go over their responses in class.

Extension suggestions: 

Extensions:

Probability in Advertising

  • Ask students to look at newspapers and magazines for examples of how numbers are used in advertisements. For example, it is not unusual to see something like "two-thirds less fat than the other leading brand" or "four out of five dentists recommend Brand T gum for their patients who chew gum." Why do advertisers use numbers like these? What information are they trying to convey? Do students think that the numbers give accurate information about a product? Why or why not?

They Said What?

  • Ask students to look at newspapers or magazines for examples of how politicians, educators, environmentalists, or others use data such as statistics and probability. Then have them analyze the use of the information. Why did the person use data? What points were effectively made? Were the data useful? Did the data strengthen the argument? Have students provide evidence to support their ideas.

Helpful Hints

Materials:

The class will need the following:

  • Understanding: Probability and Odds video
  • Copies of Classroom Activity Sheet: Probability Problem Solving
  • Computers with Internet access (optional but very helpful)
  • Reference materials such as almanacs and encyclopedias
  • Copies of Take-Home Activity Sheet: Spin the Wheel!

References

Contributors: