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The events A = "the person is a female with a smart phone" and B = "the person is a male" are 1) mutually exclusive 2) independent

The events A = "the person is a female with a smart phone" and B = "the person is a male" are 1) mutually exclusive 2) independent

MATLAB: An Introduction with Applications
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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**Classification of Events in Probability** Given the following events: - Event A: "the person is a female with a smartphone" - Event B: "the person is a male" The question is to classify the relationship between these two events. The options provided are: 1. **Mutually Exclusive:** - Events A and B cannot happen at the same time. If a person is a male, they cannot be a female with a smartphone and vice versa. 2. **Independent:** - Events A and B have no influence on each other. The occurrence of one event does not affect the probability of the other. 3. **None of the above:** - The relationship between events A and B does not fit the descriptions of being mutually exclusive or independent. **Explanation:** - **Mutually Exclusive:** For events to be mutually exclusive, if one event occurs, the other cannot. Here, if someone is male (Event B), they cannot be a female with a smartphone (Event A). Therefore, events A and B are mutually exclusive. - **Independent:** For events to be independent, the occurrence of one event should not affect the probability of the other. However, knowing someone is a male directly affects the probability of them being a female, thus these events are not independent. - **Conclusion:** Based on the above explanation, the correct classification is that events A and B are mutually exclusive. **Correct Answer:** 1) Mutually exclusive
Transcribed Image Text:**Classification of Events in Probability** Given the following events: - Event A: "the person is a female with a smartphone" - Event B: "the person is a male" The question is to classify the relationship between these two events. The options provided are: 1. **Mutually Exclusive:** - Events A and B cannot happen at the same time. If a person is a male, they cannot be a female with a smartphone and vice versa. 2. **Independent:** - Events A and B have no influence on each other. The occurrence of one event does not affect the probability of the other. 3. **None of the above:** - The relationship between events A and B does not fit the descriptions of being mutually exclusive or independent. **Explanation:** - **Mutually Exclusive:** For events to be mutually exclusive, if one event occurs, the other cannot. Here, if someone is male (Event B), they cannot be a female with a smartphone (Event A). Therefore, events A and B are mutually exclusive. - **Independent:** For events to be independent, the occurrence of one event should not affect the probability of the other. However, knowing someone is a male directly affects the probability of them being a female, thus these events are not independent. - **Conclusion:** Based on the above explanation, the correct classification is that events A and B are mutually exclusive. **Correct Answer:** 1) Mutually exclusive
**Title: Survey Results on Smartphone Ownership** A survey was conducted with 100 participants to determine smartphone ownership. Participants were categorized by gender, and the results are summarized in the table below. The table shows the number of females and males who own or do not own a smartphone. | | Female | Male | Total | |--------------------|--------|------|-------| | Owns a smartphone | 46 | 24 | 70 | | Does not own a smartphone | 18 | 12 | 30 | | Totals | 64 | 36 | 100 | **Explanation:** - **Owns a smartphone:** Out of the 70 individuals who own a smartphone, 46 are females and 24 are males. - **Does not own a smartphone:** Among the 30 individuals who do not own a smartphone, 18 are females and 12 are males. - The total number of survey participants is 100, with 64 females and 36 males. This data can help in understanding the distribution of smartphone ownership among different genders in the surveyed population.
Transcribed Image Text:**Title: Survey Results on Smartphone Ownership** A survey was conducted with 100 participants to determine smartphone ownership. Participants were categorized by gender, and the results are summarized in the table below. The table shows the number of females and males who own or do not own a smartphone. | | Female | Male | Total | |--------------------|--------|------|-------| | Owns a smartphone | 46 | 24 | 70 | | Does not own a smartphone | 18 | 12 | 30 | | Totals | 64 | 36 | 100 | **Explanation:** - **Owns a smartphone:** Out of the 70 individuals who own a smartphone, 46 are females and 24 are males. - **Does not own a smartphone:** Among the 30 individuals who do not own a smartphone, 18 are females and 12 are males. - The total number of survey participants is 100, with 64 females and 36 males. This data can help in understanding the distribution of smartphone ownership among different genders in the surveyed population.
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