Probability – Activity Directions

Set the Stage

Have students move into their teams of 2-3 before getting started. Make sure each student has a copy of the Probability Handout. If students will create their products offline, make supplies available to them. If they will create their products online, they will need an Internet connected device.

Explain to students that the term probability refers to how likely it is that an event will occur. Caution them that at the same time, the term probability can be used in different ways to mean different things. When it comes to figuring out if statements based on how probable something might be, it’s important to understand a few basics about different types of probability.

Before beginning this activity, tell students they will first take a few minutes to talk with their team members about the differences between the meanings of the words plausibility and probability. If your students completed the Unbelievable! activity on this website, remind them about that experience and ask them what they remember about the meaning of the term plausibility. If they did not complete that activity, tell them they will be looking up the definition.

Direct students’ attention to the Plausibility and Probability section of the Probability Handout. Review the directions for that section with students and give them a few minutes to research and write original definitions for both terms and then to explain how the two are different from one another.

The important point for students to grasp in this segment of the activity is that something that’s plausible may or may not be probable.

Instruction

Explain to students that while probability refers to making predictions about how likely it is that something will happen, there are different types of probabilities. Some predictions can be made with reasonable assurance that they will be accurate, but others are nothing more than educated guesses. Well-informed consumers of media may not have a deep understanding of statistics, but if they understand the basic idea behind different kinds of probabilities, will be able to recognize how reliable the numbers being reported may be.

Tell students you will review four of the common types of probability with them. Working in their teams, they will define each type of probability and list a few examples for each. They will use this information to create a quick start guide that can help others decide how accurate predictions may be. This product may be a flyer, pamphlet, video, poster, infographic, or other format approved by the teacher.

Here are the terms students need to know and understand to complete this assignment:

Types of Probabilities:

1. Classical Probability

In this type of probability, the event being predicted has equal odds of happening every time. Typical examples include rolling dice, flipping a coin, or pulling a playing card from a deck. As long as the die, coin, or deck have not been tampered with, your odds of any outcome are equal. In other words, it’s equally likely you will roll 1, 2, 3, 4, 5, or 6 with the die, get heads or tails on the coin, or have a one in 52 chance of pulling one specific card from the deck.

2. Frequency Probability

This type of probability relies on being able to conduct experiments where we can control variables and conditions in order to observe and count outcomes. Drug trials conducted by medical professionals to determine how effective a new medication will be or using last year’s merchandise ordering and sales records to predict what goods should be ordered this year are real world examples of frequency probability.

3. Subjective Probability

Subjective probability is not based on an experiment or an event that can be replicated. Instead, it relies on someone’s opinion. When a pundit appears on a news program and expresses an opinion about how an election will turn out, that’s all it is—an opinion. S/he has no way of knowing for sure what will happen. Weather reports are another example of subjective probability. When a forecaster states there is a 40% chance of rain, that simply means that on 40 out of 100 days, all other conditions being equal, it will rain. It also means that on 60 out of 100 days given the same conditions, it will not rain.

4. Conditional Probability

Conditional probability helps us describe how one or more events impact another. For example, it might be difficult to predict how many adults over the age of 50 will one day contract shingles, but if you know how many adults aged 50 and older have had chicken pox (first event) and how many of those adults have not received the shingles vaccination (second event) you may be able to predict how many of those adults are likely to get shingles in the future. Students need to understand that it’s common for statements made in the media to be based on use of conditional probability and that may not be clearly explained. So, when they read that Democrats are most likely to win elections where there is high voter turnout (conditional event) or that people are more likely to lose weight when they get 8 hours of sleep nightly (conditional event) they need to ask questions about the basis for that prediction and not take it at face value.

Before explaining the kinds of probabilities listed above, point out that the handout provides an organizer for students to write definitions of terms and examples cited during instruction.

Once you have shared the information above about kinds of probabilities, help students brainstorm ideas for additional examples of each type of probability presented in this lesson. Ask students to add these ideas to their organizers.

Guided Practice

Direct students’ attention to the Guided Practice section of the handout. Explain that student teams will work together to plan and create a quick start guide meant to help others decide if predictions they encounter in the media are likely to be accurate. These products may be in print, video, poster, infographic, or other format approved by the teacher.

Ask teams to decide what type of quick start guide they would like to create and then to plan how they will explain classical probability in the quick start guide. The Guided Practice section of the handout provides space for planning.

Each team needs to meet with you to review their product ideas for classical probability before they plan the remaining pieces of their product.

Independent Practice

Once they have your approval, student teams finish planning their products and then create them. The amount of time required for this will be determined by the complexity of each product.

Each team presents their product. If possible, make the quick start guides available to a genuine audience. Post them on your class website, ask the school librarian to make them available to other students, or check with your local public library to see if the guides can be shared there.

Possible Modification:

Depending on your students’ skill levels and available time, you may decide to reduce the number of probability types from four to three or to assign teams one or two probability types, ensuring that all four types are covered.

Probability