Apple products have become a household name in America. Suppose that the likelihood of owning an Apple product is 81% for households with kids and 55% for households without kids. Suppose there are 1,380 households in a representative community, of which 760 are with kids and the rest are without kids. Let event A correspond to "Household with kids", and B to "Household owns an Apple product". a. Are the events "household with kids" and "household without kids" mutually exclusive and exhaustive? O Yes No b. What is the probability that a household is without kids? Note: Round your answer to 4 decimal places. Probability c. What is the probability that a household is with kids and owns Apple product? Note: Do not round intermediate calculations. Round your answer to 4 decimal places. P(ANB) d. What is the probability that a household is without kids and does not own an Apple product? Note: Do not round intermediate calculations. Round your answer to 4 decimal places. Probability
Apple products have become a household name in America. Suppose that the likelihood of owning an Apple product is 81% for households with kids and 55% for households without kids. Suppose there are 1,380 households in a representative community, of which 760 are with kids and the rest are without kids. Let event A correspond to "Household with kids", and B to "Household owns an Apple product". a. Are the events "household with kids" and "household without kids" mutually exclusive and exhaustive? O Yes No b. What is the probability that a household is without kids? Note: Round your answer to 4 decimal places. Probability c. What is the probability that a household is with kids and owns Apple product? Note: Do not round intermediate calculations. Round your answer to 4 decimal places. P(ANB) d. What is the probability that a household is without kids and does not own an Apple product? Note: Do not round intermediate calculations. Round your answer to 4 decimal places. Probability
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Probability and Apple Product Ownership in Households
Apple products have become a household name in America. Suppose that the likelihood of owning an Apple product is 81% for households with kids and 55% for households without kids. Suppose there are 1,380 households in a representative community, of which 760 are with kids and the rest are without kids. Let event A correspond to “Household with kids”, and B to “Household owns an Apple product”.
---
**a. Are the events “household with kids” and “household without kids” mutually exclusive and exhaustive?**
- Yes
- No (selected)
---
**b. What is the probability that a household is without kids?**
*Note: Round your answer to 4 decimal places.*
- Probability:
---
**c. What is the probability that a household is with kids and owns an Apple product?**
*Note: Do not round intermediate calculations. Round your answer to 4 decimal places.*
- P(A ∩ B):
---
**d. What is the probability that a household is without kids and does not own an Apple product?**
*Note: Do not round intermediate calculations. Round your answer to 4 decimal places.*
- Probability:
---
### Explanation of Events and Notations
- **Event A:** Household with kids
- **Event B:** Household owns an Apple product
### Additional Information
1. **Mutually Exclusive Events:** Two events are mutually exclusive if they cannot occur at the same time.
2. **Exhaustive Events:** Two events are exhaustive if their union covers all possible outcomes in the sample space.
### Detailed Questions Breakdown
#### Question b:
To find the probability that a household is without kids:
\[ P(\text{household is without kids}) = \frac{\text{Number of households without kids}}{\text{Total number of households}} \]
#### Question c:
To find the probability that a household is with kids and owns an Apple product:
\[ P(A \cap B) = P(A) \times P(B|A) \]
where:
- \( P(A) \): Probability that a household has kids.
- \( P(B|A) \): Probability that a household with kids owns an Apple product.
#### Question d:
To find the probability that a household is without kids and does not own an Apple product:
\[ P(\text{household is without kids and does not own](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f0859e7-177f-4240-afbd-ef50c8003c62%2F16529ef5-9674-48ca-92fc-9fe9a6ce16ed%2Faod08rc_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability and Apple Product Ownership in Households
Apple products have become a household name in America. Suppose that the likelihood of owning an Apple product is 81% for households with kids and 55% for households without kids. Suppose there are 1,380 households in a representative community, of which 760 are with kids and the rest are without kids. Let event A correspond to “Household with kids”, and B to “Household owns an Apple product”.
---
**a. Are the events “household with kids” and “household without kids” mutually exclusive and exhaustive?**
- Yes
- No (selected)
---
**b. What is the probability that a household is without kids?**
*Note: Round your answer to 4 decimal places.*
- Probability:
---
**c. What is the probability that a household is with kids and owns an Apple product?**
*Note: Do not round intermediate calculations. Round your answer to 4 decimal places.*
- P(A ∩ B):
---
**d. What is the probability that a household is without kids and does not own an Apple product?**
*Note: Do not round intermediate calculations. Round your answer to 4 decimal places.*
- Probability:
---
### Explanation of Events and Notations
- **Event A:** Household with kids
- **Event B:** Household owns an Apple product
### Additional Information
1. **Mutually Exclusive Events:** Two events are mutually exclusive if they cannot occur at the same time.
2. **Exhaustive Events:** Two events are exhaustive if their union covers all possible outcomes in the sample space.
### Detailed Questions Breakdown
#### Question b:
To find the probability that a household is without kids:
\[ P(\text{household is without kids}) = \frac{\text{Number of households without kids}}{\text{Total number of households}} \]
#### Question c:
To find the probability that a household is with kids and owns an Apple product:
\[ P(A \cap B) = P(A) \times P(B|A) \]
where:
- \( P(A) \): Probability that a household has kids.
- \( P(B|A) \): Probability that a household with kids owns an Apple product.
#### Question d:
To find the probability that a household is without kids and does not own an Apple product:
\[ P(\text{household is without kids and does not own
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