Roy has a bag containing green, blue, red, brown, and black marbles. He randomly picks a marble and replaces it. He repeats this experiment 60 times and records the results in this table.

Marble Color	Times Picked
green	
18
blue	
6
red	
21
brown	
9
black	
6
The relative frequency of picking a green marble is 
.
The relative frequency of picking a blue marble is 
.
The relative frequency of picking a red marble is 
.
The relative frequency of picking a brown marble is 
.
The relative frequency of picking a black marble is 
.
All of the outcomes 
 be considered equally likely.

To calculate the relative frequency for each marble color, you divide the number of times each color was picked by the total number of trials (60). Here are the relative frequencies for each marble color:

1. **Relative frequency of picking a green marble:**
   \[
   \frac{18}{60} = 0.3
   \]

2. **Relative frequency of picking a blue marble:**
   \[
   \frac{6}{60} = 0.1
   \]

3. **Relative frequency of picking a red marble:**
   \[
   \frac{21}{60} = 0.35
   \]

4. **Relative frequency of picking a brown marble:**
   \[
   \frac{9}{60} = 0.15
   \]

5. **Relative frequency of picking a black marble:**
   \[
   \frac{6}{60} = 0.1
   \]

Since the relative frequencies of the different marble colors are not the same, the outcomes **cannot** be considered equally likely.

**Do you have any questions or need further details?**

Here are some additional questions you might be interested in:

1. How can you determine if the distribution of marble colors in the bag is uniform?
2. What is the probability of picking a marble of a specific color?
3. How does increasing the number of trials affect the accuracy of the relative frequencies?
4. What is the expected number of times each marble color should be picked if the outcomes are equally likely?
5. How can you calculate the standard deviation for the number of times each color is picked?

**Tip:** To get a more accurate understanding of probabilities, conduct more trials and compare the observed frequencies with the theoretical probabilities.

Learn how to calculate the relative frequencies of green, blue, red, brown, and black marbles based on recorded trials. Understand the concept of probability and its application in determining outcomes from repeated experiments. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation