Type of Juice Number Sold 10 Apple Orange Grapefruit Cranberry Tomato 18 3 2 Based on this data, if Marcel bought a juice at random, what is the probability that he bought an orange or grapefruit juice? 7. B) 5. D) 9. A) 18 20
Type of Juice Number Sold 10 Apple Orange Grapefruit Cranberry Tomato 18 3 2 Based on this data, if Marcel bought a juice at random, what is the probability that he bought an orange or grapefruit juice? 7. B) 5. D) 9. A) 18 20
A First Course in Probability (10th Edition)
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### Juice Sales Data and Probability Calculation
#### Juice Sales Before School
The chart below represents the number of juices sold in the cafeteria before school one morning:
| **Type of Juice** | **Number Sold** |
|-------------------|-----------------|
| Apple | 10 |
| Orange | 18 |
| Grapefruit | 7 |
| Cranberry | 3 |
| Tomato | 2 |
#### Probability Question
Based on this data, if Marcel bought a juice at random, what is the probability that he bought an orange or grapefruit juice?
**Options:**
A) \( \frac{9}{20} \)
B) \( \frac{7}{18} \)
C) \( \frac{2}{5} \)
D) \( \frac{5}{8} \)
#### Solution Explanation
To calculate the probability, follow these steps:
1. **Total Number of Juices Sold**: Sum up all the numbers in the "Number Sold" column:
\[
10 + 18 + 7 + 3 + 2 = 40
\]
2. **Number of Orange and Grapefruit Juices Sold**: Add the number of orange juices and grapefruit juices sold:
\[
18 (orange) + 7 (grapefruit) = 25
\]
3. **Probability Calculation**: Divide the number of orange and grapefruit juices sold by the total number of juices sold:
\[
\frac{25}{40} = \frac{5}{8}
\]
Therefore, the correct answer is:
**D) \( \frac{5}{8} \)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9995e28-4772-45f2-adb3-a9b2581c4879%2F67af88bb-2a47-466d-8a82-66175cb4e2a4%2F1nzwbgpg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Juice Sales Data and Probability Calculation
#### Juice Sales Before School
The chart below represents the number of juices sold in the cafeteria before school one morning:
| **Type of Juice** | **Number Sold** |
|-------------------|-----------------|
| Apple | 10 |
| Orange | 18 |
| Grapefruit | 7 |
| Cranberry | 3 |
| Tomato | 2 |
#### Probability Question
Based on this data, if Marcel bought a juice at random, what is the probability that he bought an orange or grapefruit juice?
**Options:**
A) \( \frac{9}{20} \)
B) \( \frac{7}{18} \)
C) \( \frac{2}{5} \)
D) \( \frac{5}{8} \)
#### Solution Explanation
To calculate the probability, follow these steps:
1. **Total Number of Juices Sold**: Sum up all the numbers in the "Number Sold" column:
\[
10 + 18 + 7 + 3 + 2 = 40
\]
2. **Number of Orange and Grapefruit Juices Sold**: Add the number of orange juices and grapefruit juices sold:
\[
18 (orange) + 7 (grapefruit) = 25
\]
3. **Probability Calculation**: Divide the number of orange and grapefruit juices sold by the total number of juices sold:
\[
\frac{25}{40} = \frac{5}{8}
\]
Therefore, the correct answer is:
**D) \( \frac{5}{8} \)**
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