Questionditional Probability from a Table
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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?
\begin{tabular}{|c|c|c|}
\hline & Has a cat & Does not have a cat \\
\hline Has a dog & 7 & 10 \\
\hline Does not have a dog & 2 & 9 \\
\hline
\end{tabular}
Answer Attempt 1 out of 2
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Studdy Solution
STEP 1
What is this asking? Out of all the students who have a dog, how many *also* have a cat? Watch out! Don't mix up the total number of students with the number of students who have a dog!
STEP 2
1. Find the total number of students with a dog.
2. Find the number of students with *both* a dog and a cat.
3. Calculate the probability.
STEP 3
Let's look at the row that says "Has a dog." We see **7** students have a dog *and* a cat, and **10** students have a dog but *don't* have a cat.
STEP 4
To find the *total* number of students with a dog, we **add** those two numbers together: .
So there are **17** students with a dog.
This is our **dog-owner total**!
STEP 5
This one is given to us directly in the table!
We see that **7** students have both a dog and a cat.
This is our **dog-and-cat** number!
STEP 6
Remember, probability is just a fancy way of saying "chance." We want to find the chance that a student who has a dog *also* has a cat.
STEP 7
We know that out of the **17** students with a dog (our **dog-owner total**), **7** of them *also* have a cat (our **dog-and-cat** number).
STEP 8
So, the probability is just the **dog-and-cat** number divided by the **dog-owner total**: .
STEP 9
The probability that a student who has a dog also has a cat is .
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