Use the following information for Experiments 1 and 2: A bag of M&M's was opened and the number of each color was recorded in the chart to the right.
Use the following information for Experiments 1 and 2: A bag of M&M's was opened and the number of each color was recorded in the chart to the right.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Experiment 1: Probability with M&M's**
**Objective:**
Understand and calculate basic probabilities using a real-world example involving M&M’s.
**Experiment Information:**
A bag of M&M’s was opened and the number of each color was recorded. The results are displayed in the chart below:
| COLOR | NUMBER OF EACH COLOR |
|----------|-----------------------|
| Green | 9 |
| Orange | 8 |
| Blue | 14 |
| Red | 6 |
| Yellow | 5 |
| Brown | 6 |
| **TOTAL** | **48** |
**Experiment #1:**
You reach into your pile of M&M's and pick one.
**Observation:**
Color of the M&M.
1. **Sample Space:**
The sample space (S) is the set of all possible outcomes. In this case, the sample space consists of the colors of the M&M's:
\[
S = \{ \text{Green, Orange, Blue, Red, Yellow, Brown} \}
\]
2. **N:**
The total number of M&M's in the bag, \( N \), is:
\[
N = 48
\]
3. **Number of events:**
Each event corresponds to picking an M&M of a particular color. The number of events corresponds to the count of each color:
- Green: 9
- Orange: 8
- Blue: 14
- Red: 6
- Yellow: 5
- Brown: 6
4. **List two events (simple random events):**
- Event A: Picking a Green M&M.
- Event B: Picking a Blue M&M.
**Calculation of Probabilities:**
To calculate the probability of each event (color), use the formula:
\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
- **Probability of picking a Green M&M \( P(\text{Green}) \):**
\[
P(\text{Green}) = \frac{9}{48} \approx 0.188
\]
- **Probability of picking an Orange M&M \( P(\text{Orange}) \):**
\[
P(\text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F196808f0-a3a0-4eb7-96e8-c00d109967f5%2F87d642d1-7fb2-4b39-9146-728456987e18%2Fjrkjnf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Experiment 1: Probability with M&M's**
**Objective:**
Understand and calculate basic probabilities using a real-world example involving M&M’s.
**Experiment Information:**
A bag of M&M’s was opened and the number of each color was recorded. The results are displayed in the chart below:
| COLOR | NUMBER OF EACH COLOR |
|----------|-----------------------|
| Green | 9 |
| Orange | 8 |
| Blue | 14 |
| Red | 6 |
| Yellow | 5 |
| Brown | 6 |
| **TOTAL** | **48** |
**Experiment #1:**
You reach into your pile of M&M's and pick one.
**Observation:**
Color of the M&M.
1. **Sample Space:**
The sample space (S) is the set of all possible outcomes. In this case, the sample space consists of the colors of the M&M's:
\[
S = \{ \text{Green, Orange, Blue, Red, Yellow, Brown} \}
\]
2. **N:**
The total number of M&M's in the bag, \( N \), is:
\[
N = 48
\]
3. **Number of events:**
Each event corresponds to picking an M&M of a particular color. The number of events corresponds to the count of each color:
- Green: 9
- Orange: 8
- Blue: 14
- Red: 6
- Yellow: 5
- Brown: 6
4. **List two events (simple random events):**
- Event A: Picking a Green M&M.
- Event B: Picking a Blue M&M.
**Calculation of Probabilities:**
To calculate the probability of each event (color), use the formula:
\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
- **Probability of picking a Green M&M \( P(\text{Green}) \):**
\[
P(\text{Green}) = \frac{9}{48} \approx 0.188
\]
- **Probability of picking an Orange M&M \( P(\text{Orange}) \):**
\[
P(\text{
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