# Counting Problems

Examples, videos, and solutions to help Grade 7 students solve counting problems related to computing percents.

### Lesson 1 Student Outcomes

• Students understand that a probability is a number between and that represents the likelihood that an event will occur.
• Students interpret a probability as the proportion of the time that an event occurs when a chance experiment is repeated many times.

### Lesson Summary

• Probability is a measure of how likely it is that an event will happen.
• A probability is a number between 0 and 1.

Example 1: Spinner Game

Suppose you and your friend will play a game using the spinner shown here:
Rules of the game:

1. Decide who will go first.
2. Each person picks a color. Both players cannot pick the same color.
3. Each person takes a turn spinning the spinner and recording what color the spinner stops on. The winner is the person whose color is the first to happen times.
Play the game and remember to record the color the spinner stops on for each spin.

Exercises 1–4

1. Which color was the first to occur times?
2. Do you think it makes a difference who goes first to pick a color?
3. Which color would you pick to give you the best chance of winning the game? Why would you pick that color?
4. Below are three different spinners. If you pick green for your color, which spinner would give you the best chance to win? Give a reason for your answer.

Example 2: What is Probability?
Probability is about how likely it is that an event will happen. A probability is indicated by a number between and . Some events are certain to happen, while others are impossible. In most cases, the probability of an event happening is somewhere between certain and impossible.

For example, consider a bag that contains only red balls. If you were to select one ball from the bag, you are certain to pick a red one. We say that an event that is certain to happen has a probability of 1. If we were to reach into the same bag of balls, it is impossible to select a yellow ball. An impossible event has a probability of 0.

Exercises 5–8
5. Decide where each event would be located on the scale below. Place the letter for each event on the appropriate place on the probability scale.
A. You will see a live dinosaur on the way home from school today.
B. A solid rock dropped in the water will sink.
C. A round disk with one side red and the other side yellow will land yellow side up when flipped.
D. A spinner with four equal parts numbered 1–4 will land on the on 4 the next spin.
E. Your name will be drawn when a name is selected randomly from a bag containing the names of all of the students in your class.
F. A red cube will be drawn when a cube is selected from a bag that has five blue cubes and five red cubes.
G. The temperature outside tomorrow will be –250 degrees.

6. Design a spinner so that the probability of green
7. Design a spinner so that the probability of green is 0.
8. Design a spinner with two outcomes in which it is equally likely to land on the red and green parts.

Exercises 9–10
An event that is impossible has probability 0 and will never occur, no matter how many observations you make. This means that in a long sequence of observations, it will occur 0% of the time. An event that is certain, has probability and will always occur. This means that in a long sequence of observations, it will occur 100% of the time.
9. What do you think it means for an event to have a probability of 1/2?
10. What do you think it means for an event to have a probability of 1/4?

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