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7th Grade Math / Lesson 9A: Sample Space

What will we be learning in this lesson?

  • In this lesson you will learn how to find a sample space of outcomes.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


  • There are two boxes, one with the colors red, blue, green, and white. And the other with the numbers 1, 2, and 3. Find the number of ways of picking 1 item from each box.

    One way of keeping track of this is by making an organized list.
    Pick an item to start with. Say we start with the color red. This came out of the first bag and will need to be paired up with each number in the second bag.

    Red, 1
    Red, 2
    Red, 3
    Now move on to the next color and pair that color up with each number.
    Blue, 1
    Blue, 2
    Blue, 3


Continue this for each color until you have used all of the colors.

Red, 1     blue, 1     green, 1     white, 1
Red, 2     blue, 2     green, 2     white, 2
Red, 3     blue, 3     green, 3     white, 3

This gives a complete list of all possible ways of picking one item from each bag.

Each combination listed is called an outcome. An outcome is one of the results of the event. In this case, the event is picking two items, one from each box.

The list of all outcomes is called the sample space. This event has 12 outcomes in its sample space. This means that there are 12 different ways that an item from each box can be chosen.


  • Another way to display a sample space is by making a tree diagram. Again, pick an item to start with. Then draw the "branches" that connect this item to each of the items from the other box. Do this for each item in the first box.

    The tree diagram provides the same information that the organized list does. There are 12 outcomes in this sample space.

    • Can you create a sample space for an event?
    • Go back to the classroom to get to your homework and any other items you need to attend to.