in a survey of 984 ﻿pet owners, 372 ﻿said they had a dog, 448 ﻿said they had a cat, and 211 ﻿said they had a fish. If 236 ﻿of the pet owners had only a dog, 275 ﻿only had a cat, 89 ﻿had only fish and 18 ﻿said they had all three. what is the probability that random home owner had exactly one of the pets if we know they had at least one pet? explain like you are teaching a child

Let's break down the problem step by step like we're telling a story:

---

### Step 1: Understanding the Problem
In a survey of 984 pet owners, some have dogs, some have cats, and some have fish. We want to find out how likely it is that a random pet owner **only has one type of pet** if they own at least one pet.

- **372 people** have dogs.
- **448 people** have cats.
- **211 people** have fish.

However, not everyone has just one pet. Some might have a combination of two or even all three types of pets.

---

### Step 2: Focus on the People with Exactly One Pet
We already know how many people have exactly one type of pet:

- **236 people** have only a dog.
- **275 people** have only a cat.
- **89 people** have only a fish.

So, the total number of people with exactly one type of pet is:

\[
236 + 275 + 89 = 600 \text{ people.}
\]

---

### Step 3: People with At Least One Pet
To figure out how many people have at least one pet, we need to exclude the people who don’t have any pets. The question doesn't directly tell us about people without pets, so we focus only on the pet owners in the survey. So, the total number of people with at least one pet is:

\[
984 \text{ (total pet owners)}.
\]

This means all 984 people have at least one pet.

---

### Step 4: Probability Formula
The probability of something happening is calculated like this:

\[
\text{Probability} = \frac{\text{Number of people with exactly one pet}}{\text{Number of people with at least one pet}}.
\]

Here, we know:
- The number of people with exactly one pet = **600**.
- The number of people with at least one pet = **984**.

Now we calculate the probability:

\[
\text{Probability} = \frac{600}{984} \approx 0.6098.
\]

This means there is a **60.98% chance** that a random pet owner had exactly one type of pet.

---

### Step 5: Conclusion
So, if we randomly pick one of the pet owners, the probability that they have exactly one type of pet is about **61%**.

---

Does that make sense? Would you like more details or have any questions?

Here are some related questions you can think about:

1. What is the probability that a pet owner has only a dog?
2. How many pet owners have exactly two pets?
3. How many people have exactly two of the three pets?
4. What is the probability that a pet owner has both a dog and a cat?
5. If someone doesn’t have a fish, what’s the chance they have a cat?

### Tip:
Probabilities are always between 0 and 1 (or 0% and 100%). A probability of 1 means something will definitely happen, and 0 means it won't happen at all!

In a survey of 984 ﻿pet owners, 372 ﻿said they had a dog, 448 ﻿said they had a cat, and 211 ﻿said they had a fish. If 236 ﻿of the pet owners had only a dog, 275 ﻿only had a cat, 89 ﻿had only fish and 18 ﻿said they had all three. What is the probability that a random homeowner had exactly one of the pets if we know they had at least one pet? Explain like you are teaching a child.

Explore how to calculate the probability that a random pet owner has exactly one type of pet, based on a survey of 984 pet owners. Learn key concepts like probability, sets, and Venn diagrams, using a detailed step-by-step explanation. Suitable for Grades 5-7.

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