Question

a survey was taken of children between the ages of 10 and 17 about how many siblings they have and whether they have a pet. the results of the survey are shown in the table

\

$$\begin{tabular}{|c|c|c|c|c|c|} \\hline & 0 siblings & 1 sibling & 2 siblings & 3 or more siblings & total \\\\ \\hline has a pet & 34 & 57 & & 6 & 125 \\\\ \\hline does not have a pet & 18 & & 15 & 2 & \\\\ \\hline total & & 97 & & & 200 \\\\ \\hline \\end{tabular}$$

which statement must be true?

• out of the 125 children who do not have a pet, 18 of them have 2 siblings
• out of the 97 children who have 1 pet, 40 of them do not have any siblings
• out of the 125 children who do not have any siblings, 34 of them have a pet.
• out of the 97 children who have 1 sibling, 40 of them do not have a pet.

Explanation:

Complete the two-way frequency table

Using the Two-Way Frequency Tables knowledge point

$$
LATEXBLOCK0
$$

Evaluate the first statement

The first statement says: "Out of the 125 children who do not have a pet, 18 of them have 2 siblings."

• The total number of children who do not have a pet is \(75\), not \(125\).
• The number of children who do not have a pet and have 2 siblings is \(15\).
• Therefore, this statement is false.

Evaluate the second statement

The second statement says: "Out of the 97 children who have 1 pet, 40 of them do not have any siblings."

• The number \(97\) represents the total number of children with 1 sibling, not "1 pet".
• Therefore, this statement is false.

Evaluate the third statement

The third statement says: "Out of the 125 children who do not have any siblings, 34 of them have a pet."

• The total number of children who do not have any siblings (0 siblings) is \(34 + 18 = 52\), not \(125\).
• Therefore, this statement is false.

Evaluate the fourth statement

The fourth statement says: "Out of the 97 children who have 1 sibling, 40 of them do not have a pet."

• The total number of children who have 1 sibling is indeed \(97\).
• From our completed table, the number of children who have 1 sibling and do not have a pet is \(40\).
• Therefore, this statement is true.

Answer:

• (A) Out of the 125 children who do not have a pet, 18 of them have 2 siblings
• (B) Out of the 97 children who have 1 pet, 40 of them do not have any siblings
• (C) Out of the 125 children who do not have any siblings, 34 of them have a pet.
• (D) Out of the 97 children who have 1 sibling, 40 of them do not have a pet. (Correct answer)