Questions: Fill in the following contingency table and find the number of students who both do not have a cat AND do not have a dog. Students have a dog do not have a dog Total ------------ have a cat 49 do not have a cat 20 46 Total 50 Provide your answer below:

Fill in the following contingency table and find the number of students who both do not have a cat AND do not have a dog. Students have a dog do not have a dog Total ------------ have a cat 49 do not have a cat 20 46 Total 50 Provide your answer below:
Transcript text: Fill in the following contingency table and find the number of students who both do not have a cat AND do not have a dog. \begin{tabular}{|l|l|l|l|} \hline Students & have a dog & do not have a dog & Total \\ \hline have a cat & & & 49 \\ \hline do not have a cat & 20 & & 46 \\ \hline Total & & 50 & \\ \hline \end{tabular} Provide your answer below: $\square$
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Solution

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Solution Steps

To solve this problem, we need to fill in the missing values in the contingency table and then find the number of students who neither have a cat nor a dog. We can use the given totals to determine the missing values.

  1. Use the total number of students who have a cat and the total number of students who do not have a cat to find the total number of students.
  2. Use the total number of students who have a dog and the total number of students who do not have a dog to find the total number of students.
  3. Use the totals to fill in the missing values in the table.
  4. Calculate the number of students who neither have a cat nor a dog.
Step 1: Calculate Total Number of Students

Given: \[ \text{Total students who have a cat} = 49 \] \[ \text{Total students who do not have a cat} = 46 \] \[ \text{Total students} = 49 + 46 = 95 \]

Step 2: Calculate Students Who Have Both a Cat and a Dog

Given: \[ \text{Total students who have a dog} = 50 \] \[ \text{Total students} = 95 \] \[ \text{Students who have a cat and a dog} = 49 - (95 - 50) = 49 - 45 = 4 \]

Step 3: Calculate Students Who Have a Cat and Do Not Have a Dog

\[ \text{Students who have a cat and do not have a dog} = 49 - 4 = 45 \]

Step 4: Calculate Students Who Do Not Have a Cat and Have a Dog

\[ \text{Students who do not have a cat and have a dog} = 50 - 4 = 46 \]

Step 5: Calculate Students Who Neither Have a Cat Nor a Dog

\[ \text{Students who do not have a cat and do not have a dog} = 46 - 46 = 0 \]

Final Answer

\[ \boxed{0} \]

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