Examples, videos, and solutions to help Grade 7 students learn how to determine the possible outcomes for simple chance experiments.
• Students learn how to determine the possible outcomes for simple chance experiments.
• Given a description of a simple chance experiment, students determine the sample space for the experiment.
• Given a description of a chance experiment and an event, students determine for which outcomes in the sample space the event will occur.
• Students distinguish between chance experiments with equally likely outcomes and chance experiments for which the outcomes are not equally likely.
Lesson 3 Classwork
Example 1 Jamal, a 7th grader, wants to design a game that involves tossing paper cups. Jamal tosses a paper cup five times and records the outcome of each toss. An outcome is the result of a single trial of an experiment.
Here are the results of each toss:
Jamal noted that the paper cup could land in one of three ways: on its side, right side up, or upside down. The collection of these three outcomes is called the sample space of the experiment. The sample space of an experiment is the set of all possible outcomes of that experiment.
For example, the sample space when flipping a coin is Heads, Tails.
The sample space when drawing a colored cube from a bag that has red, blue, yellow, and green cubes is red, blue, yellow, green.
For each of the following chance experiments, list the sample space (i.e., all the possible outcomes).
Example 2: Equally Likely Outcomes
The sample space for the paper cup toss was on its side, right side up, and upside down. Do you think each of these outcomes has the same chance of occurring? If they do, then they are equally likely to occur.
The outcomes of an experiment are equally likely to occur when the probability of each outcome is equal. You and your partner toss the paper cup 30 times and record in a table the results of each toss.
7. Using the results of your experiment, what is your estimate for the probability of a paper cup landing on its side?
8. Using the results of your experiment, what is your estimate for the probability of a paper cup landing upside down?
9. Using the results of your experiment, what is your estimate for the probability of a paper cup landing right side up?
10. Based on your results, do you think the three outcomes are equally likely to occur?
11. Using the spinner below, answer the following questions.
a. Are the events spinning and landing on 1 or a 2 equally likely? b. Are the events spinning and landing on 2 or 3 equally likely?
c. How many times do you predict the spinner to land on each section after 100 spins? 12. Draw a spinner that has 3 sections that are equally likely to occur when the spinner is spun. How many times do you think the spinner will land on each section after 100 spins?
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