What Are Probabilities?

5 min

Teacher Prep
Setup
Students in groups of 2. 1 minute of quiet work time followed by partner and whole-class discussions.

Narrative

The purpose of this Warm-up is for students to choose the more likely event based on their intuition about the possible outcomes of two chance experiments. The activities in this lesson that follow define probability and give ways to compute numerical values for the probability of chance events such as these.

Launch

Arrange students in groups of 2. Give students 1 minute of quiet work time followed by time to share their response with a partner. Follow with a whole-class discussion. 

Student Task

Which game are you more likely to win? Explain your reasoning.

Game 1: You flip a coin and win if it lands showing heads.

Game 2: You roll a standard number cube and win if it lands showing a number that is divisible by 3.

Sample Response

Sample response: I would rather play Game 1 since I have 1 out of 2 ways to win, which is half of the time. In Game 2, I only have 2 out of 6 ways to win.

Activity Synthesis (Teacher Notes)

Have partners share their answers and display the results for all to see. Select at least 1 student for each answer provided to give a reason for their choice. 

If no student mentions it, explain that the number of possible outcomes that count as a win and the number of total possible outcomes are both important to determining the likelihood of an event. That is, although there are 2 ways to win with the standard number cube and only 1 way to win on the coin, the greater number of possible outcomes in the second game makes it less likely to provide a win.

Anticipated Misconceptions

Some students may have trouble comparing 12\frac{1}{2} and 26\frac{2}{6}. Ask students how they might write these values as decimals or to draw a shape and divide it into 6 equal regions, then think of what it would look like to shade half of the regions or 26\frac{2}{6} of the regions.

Some students may struggle with the wording of the second game. Help them understand what it means for a number to be divisible by a certain number and consider providing them with a standard number cube to examine the possible values.

Standards
Addressing
  • 7.SP.5·Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
  • 7.SP.7.a·Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. <em>For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.</em>
  • 7.SP.C.5·Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
  • 7.SP.C.7.a·Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. <span>For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.</span>

15 min

15 min