 # Calculating Probabilities for Chance Experiments

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Example, videos, and solutions to help Grade 7 students learn how to calculate probabilities of events for chance experiments that have equally likely outcomes.

### New York State Common Core Math Grade 7, Module 5, Lesson 4

Download worksheets for Grade 7, Module 5, Lesson 4

### Lesson 4 Student Outcomes

• Students will calculate probabilities of events for chance experiments that have equally likely outcomes.

### Lesson 4 Summary

When all the possible outcomes of an experiment are equally likely, the probability of each outcome is
P(outcome) = 1/number of possible outcomes

An event is a collection of outcomes, and when all outcomes are equally likely, the theoretical probability of an event can be expressed as
P(event) = Number of favorable outcomes/Number of possible outcomes

Lesson 4 Classwork

Example 1: Theoretical Probability
In a previous lesson, you saw that to find an estimate of the probability of an event for a chance experiment you divide:
P(event) = Number of observed occurrences of the event/Total number of observations

Your teacher has a bag with some cubes colored yellow, green, blue, and red. The cubes are identical except for their color. Your teacher will conduct a chance experiment by randomly drawing a cube with replacement from the bag. Record the outcome of each draw in the table below.
Exercises 1–6
1. Based on the 20 trials, estimate for the probability of
a. choosing a yellow cube.
b. choosing a green cube.
c. choosing a red cube.
d. choosing a blue cube.

2. If there are cubes in the bag, how many cubes of each color are in the bag? Explain.

3. If your teacher were to randomly draw another 20 cubes one at a time and with replacement from the bag, would you see exactly the same results? Explain.

4. Find the fraction of each color of cubes in the bag.

Each fraction is the theoretical probability of choosing a particular color of cube when a cube is randomly drawn from the bag.
When all the possible outcomes of an experiment are equally likely, the probability of each outcome is
P(outcome) = 1/number of possible outcomes

An event is a collection of outcomes, and when the outcomes are equally likely, the theoretical probability of an event can be expressed as
P(event) = Number of favorable outcomes/Number of possible outcomes

The theoretical probability of drawing a blue cube is
P(blue) = Number of blue cubes/Total number of cubes = 10/40

5. Is each color equally likely to be chosen? Explain your answer.

6. How do the theoretical probabilities of choosing each color from Exercise 4 compare to the experimental probabilities you found in Exercise 1?

Example 2
An experiment consisted of flipping a nickel and a dime. The first step in finding the theoretical probability of obtaining a head on the nickel and a head on the dime is to list the sample space. For this experiment, the sample space is shown below.
If the counts are fair, these outcomes are equally likely, so the probability of each outcome is 1/4.
The probability of two heads is 1/4 or P(two heads) = 1/4

Exercises 7–10
7. Consider a chance experiment of rolling a number cube.
a. What is the sample space? List the probability of each outcome in the sample space.
b. What is the probability of rolling an odd number?
c. What is the probability of rolling a number less than 5?

8. Consider an experiment of randomly selecting a letter from the word: number.
a. What is the sample space? List the probability of each outcome in the sample space.
b. What is the probability of selecting a vowel?
c. What is the probability of selecting the letter z?

9. Consider an experiment of randomly selecting a cube from a bag of 10 cubes.
a. Color the cubes below so that the probability of selecting a blue cube is 1/2.
b. Color the cubes below so that the probability of selecting a blue cube is 4/5.

10. Students are playing a game that requires spinning the two spinners shown below. A student wins the game if both spins land on Red. What is the probability of winning the game? Remember to first list the sample space and the probability of each outcome in the sample space. There are eight possible outcomes to this chance experiment.

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