A Veterinarian Surveys Her Clients And Finds That 32 Percent Of The Households Have Dogs, 25 Percent Have Cats, And 11 Percent Have Both Dogs And Cats. Let Event C Be Choosing A Client Who Has Cats, And Let Event D Be Choosing A Client Who Has

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Introduction

As a veterinarian, it is essential to understand the demographics of pet ownership in a given area. This information can help inform decisions about animal care services, marketing strategies, and community outreach programs. In this article, we will explore the results of a survey conducted by a veterinarian, which reveals the percentage of households with dogs, cats, and both pets.

The Survey Results

The survey found that 32 percent of households have dogs, 25 percent have cats, and 11 percent have both dogs and cats. These numbers provide a snapshot of the pet ownership landscape in the area, but they also raise interesting questions about the relationships between these events.

Defining the Events

Let's define two events:

  • Event C: Choosing a client who has cats
  • Event D: Choosing a client who has dogs

These events are not mutually exclusive, as some households may have both cats and dogs. In fact, 11 percent of households have both pets.

Understanding the Probability of Event C

The probability of event C (choosing a client who has cats) is given by the percentage of households with cats, which is 25 percent. This can be represented mathematically as:

P(C) = 0.25

Understanding the Probability of Event D

The probability of event D (choosing a client who has dogs) is given by the percentage of households with dogs, which is 32 percent. This can be represented mathematically as:

P(D) = 0.32

Understanding the Probability of Both Events

The probability of both events C and D occurring is given by the percentage of households with both cats and dogs, which is 11 percent. This can be represented mathematically as:

P(C ∩ D) = 0.11

The Relationship Between the Events

The events C and D are not mutually exclusive, as some households may have both cats and dogs. This means that the probability of event C and event D occurring together is not simply the product of their individual probabilities. Instead, we need to use the formula for the probability of the intersection of two events:

P(C ∩ D) = P(C) + P(D) - P(C ∪ D)

where P(C ∪ D) is the probability of either event C or event D occurring.

Calculating the Probability of the Union of the Events

To calculate the probability of the union of the events C and D, we need to add the probabilities of the individual events and subtract the probability of the intersection of the events:

P(C ∪ D) = P(C) + P(D) - P(C ∩ D) = 0.25 + 0.32 - 0.11 = 0.46

The Final Answer

So, what can we conclude from this survey? The probability of choosing a client who has cats is 25 percent, while the probability of choosing a client who has dogs is 32 percent. The probability of choosing a client who has both cats and dogs is 11 percent. By understanding the relationships between these events, we can gain a deeper insight into the demographics of pet ownership in the area.

Conclusion

In conclusion, the survey conducted by the veterinarian provides valuable insights into the demographics of pet ownership in the area. By understanding the probabilities of the events C and D, we can gain a deeper insight into the relationships between these events and make informed decisions about animal care services, marketing strategies, and community outreach programs.

References

  • [1] "Survey Results: Pet Ownership in the Area." Veterinarian's Office, 2023.
  • [2] "Probability Theory." Wikipedia, 2023.

Further Reading

For more information on probability theory and its applications, please see the following resources:

  • [1] "Probability Theory." Khan Academy, 2023.
  • [2] "Statistics and Probability." Coursera, 2023.

Glossary

  • Event C: Choosing a client who has cats
  • Event D: Choosing a client who has dogs
  • Probability: A measure of the likelihood of an event occurring
  • Mutually Exclusive Events: Events that cannot occur together
  • Union of Events: The combination of two or more events
  • Intersection of Events: The combination of two or more events that occur together
    A Veterinarian's Survey: Understanding the Probability of Pet Ownership ===========================================================

Q&A: Understanding the Probability of Pet Ownership

Q: What is the probability of choosing a client who has cats?

A: The probability of choosing a client who has cats is 25 percent, or 0.25.

Q: What is the probability of choosing a client who has dogs?

A: The probability of choosing a client who has dogs is 32 percent, or 0.32.

Q: What is the probability of choosing a client who has both cats and dogs?

A: The probability of choosing a client who has both cats and dogs is 11 percent, or 0.11.

Q: Why is it important to understand the probability of pet ownership?

A: Understanding the probability of pet ownership is essential for veterinarians, animal care services, and community outreach programs. It helps inform decisions about marketing strategies, animal care services, and community outreach programs.

Q: What is the relationship between the events C and D?

A: The events C and D are not mutually exclusive, as some households may have both cats and dogs. This means that the probability of event C and event D occurring together is not simply the product of their individual probabilities.

Q: How do I calculate the probability of the union of the events C and D?

A: To calculate the probability of the union of the events C and D, you need to add the probabilities of the individual events and subtract the probability of the intersection of the events:

P(C ∪ D) = P(C) + P(D) - P(C ∩ D) = 0.25 + 0.32 - 0.11 = 0.46

Q: What is the probability of the union of the events C and D?

A: The probability of the union of the events C and D is 46 percent, or 0.46.

Q: Why is it important to understand the probability of the union of the events C and D?

A: Understanding the probability of the union of the events C and D is essential for veterinarians, animal care services, and community outreach programs. It helps inform decisions about marketing strategies, animal care services, and community outreach programs.

Q: Can I use the probability of the union of the events C and D to make decisions about animal care services?

A: Yes, you can use the probability of the union of the events C and D to make decisions about animal care services. For example, if you are a veterinarian, you can use this probability to determine the likelihood of a client having a cat or a dog, and adjust your marketing strategies accordingly.

Q: Can I use the probability of the union of the events C and D to make decisions about community outreach programs?

A: Yes, you can use the probability of the union of the events C and D to make decisions about community outreach programs. For example, if you are a community outreach program, you can use this probability to determine the likelihood of a household having a cat or a dog, and adjust your outreach strategies accordingly.

Q: Where can I find more information about probability theory and its applications?

A: You can find more information about probability theory and its applications on the following resources:

  • [1] "Probability Theory." Khan Academy, 2023.
  • [2] "Statistics and Probability." Coursera, 2023.

Glossary

  • Event C: Choosing a client who has cats
  • Event D: Choosing a client who has dogs
  • Probability: A measure of the likelihood of an event occurring
  • Mutually Exclusive Events: Events that cannot occur together
  • Union of Events: The combination of two or more events
  • Intersection of Events: The combination of two or more events that occur together