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In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a dog also has a cat?
Has a cat Does not have a cat
Has a dog 6 2
Does not have a dog 14 8
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In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a dog also has a cat?
Has a cat Does not have a cat
Has a dog 6 2
Does not have a dog 14 8
Answer
Attempt 1 out of 2
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GPT-4o mini
To find the probability that a student who has a dog also has a cat, we need to focus on the students who have dogs.
From the data table, we see that:
- The number of students who have both a dog and a cat is 6.
- The number of students who have a dog but do not have a cat is 2.
To find the probability that a student who has a dog also has a cat, we use the formula:
\[
P(\text{has a cat} | \text{has a dog}) = \frac{\text{Number of students with a dog and a cat}}{\text{Total number of students with a dog}}
\]
Let's calculate it:
1. The total number of students who have a dog:
- Students with a dog and a cat: 6
- Students with a dog but without a cat: 2
- Total with a dog = 6 + 2 = 8
2. The number of students who have a dog and a cat: 6
Now, plugging these numbers into the formula gives:
\[
P(\text{has a cat} | \text{has a dog}) = \frac{6}{8} = \frac{3}{4}
\]
So, the probability that a student who has a dog also has a cat is \( \frac{3}{4} \) or 0.75.
From the data table, we see that:
- The number of students who have both a dog and a cat is 6.
- The number of students who have a dog but do not have a cat is 2.
To find the probability that a student who has a dog also has a cat, we use the formula:
\[
P(\text{has a cat} | \text{has a dog}) = \frac{\text{Number of students with a dog and a cat}}{\text{Total number of students with a dog}}
\]
Let's calculate it:
1. The total number of students who have a dog:
- Students with a dog and a cat: 6
- Students with a dog but without a cat: 2
- Total with a dog = 6 + 2 = 8
2. The number of students who have a dog and a cat: 6
Now, plugging these numbers into the formula gives:
\[
P(\text{has a cat} | \text{has a dog}) = \frac{6}{8} = \frac{3}{4}
\]
So, the probability that a student who has a dog also has a cat is \( \frac{3}{4} \) or 0.75.
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