syaoranig
Answered

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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 has a dog given that they have a cat?

\begin{tabular}{|c|c|c|}
\hline
& \begin{tabular}{c}
Has a \\
cat
\end{tabular} & \begin{tabular}{c}
Does not have \\
a cat
\end{tabular} \\
\hline
Has a dog & 6 & 7 \\
\hline
\begin{tabular}{c}
Does not have \\
a dog
\end{tabular} & 9 & 4 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To find the probability that a student has a dog given that they have a cat, we follow these steps:

1. Identify the relevant data from the table:
- The number of students who have both a cat and a dog: [tex]\(6\)[/tex]
- The number of students who have a cat but not a dog: [tex]\(9\)[/tex]

2. Calculate the total number of students who have a cat:
- This is the sum of students who have a cat and a dog, and students who have a cat but not a dog:
[tex]\[ \text{Total students who have a cat} = 6 + 9 = 15 \][/tex]

3. Apply the formula for conditional probability:
- The probability that a student has a dog given that they have a cat is given by the ratio of the number of students who have both a cat and a dog to the total number of students who have a cat.
[tex]\[ P(\text{Dog} | \text{Cat}) = \frac{\text{Number of students who have both a cat and a dog}}{\text{Total number of students who have a cat}} \][/tex]

4. Substitute the values into the formula:
- Number of students who have both a cat and a dog: [tex]\(6\)[/tex]
- Total number of students who have a cat: [tex]\(15\)[/tex]
[tex]\[ P(\text{Dog} | \text{Cat}) = \frac{6}{15} = 0.4 \][/tex]

Therefore, the probability that a student has a dog given that they have a cat is [tex]\(0.4\)[/tex] or [tex]\(40\%\)[/tex].
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