Chance Experiments with Equally Likely Outcomes

Lesson 3 Student Outcomes

• 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 Summary

An outcome is the result of a single observation of an experiment.
The sample space of an experiment is the set of all possible outcomes of that experiment.
The outcomes of an experiment are equally likely to occur when the probability of each outcome is equal.
Suppose a bag of crayons contains 10 green, 10 red, 10 yellow, 10 orange, and 10 purple pieces of crayons. If one crayon is selected from the bag and the color is noted, the outcome is the color that will be chosen. The sample space will be the colors: green, red, yellow, orange, and purple. Each color is equally likely to be selected because each color has the same chance of being chosen.

Sample Questions

1. For each of the following chance experiments, list the sample space (i.e., all the possible outcomes).
a. Rolling a 6-sided dice with numbers 1-6 on the faces of the die.

b. Selecting a letter from the word: LESSON

c. Selecting a marble from a bag containing 20 red marbles and 10 blue marbles.

2. For each of the following decide if the two outcomes listed are equally likely to occur. Give a reason for your answer.
a. Rolling an even number or an odd number when a 6-sided number cube with the numbers 1 – 6 on the faces of the cube is rolled.
b. Selecting the letter L or N from the word: LESSON.
c. Selecting a red or blue marble from a bag containing 20 red marbles and 10 blue marbles.

3. Color the cubes below so that it would be equally likely to choose a blue or yellow cube.

4. Color the cubes below so that it would be more likely to choose a red than a black cube.

5. You are playing a game using the spinner below. The game requires that you spin the spinner twice. For example, one outcome could be Yellow on 1st spin and Red on 2nd spin. spin. List the sample space (all the possible outcomes) for the two spins.

6. List the sample space for the chance experiment of flipping a coin twice.