Question

students in a class were surveyed about the number of children in their families. the results of the survey are shown in the table

\

$$\begin{tabular}{|c|c|} \\hline \\text{number of children in family} & \\text{number of surveys} \\\\ \\hline \\text{one} & 9 \\\\ \\hline \\text{two} & 18 \\\\ \\hline \\text{three} & 22 \\\\ \\hline \\text{four} & 8 \\\\ \\hline \\text{five or more} & 3 \\\\ \\hline \\end{tabular}$$

two surveys are chosen at random from the group of surveys. after the first survey is chosen, it is returned to the stack and can be chosen a second time. what is the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family?

(a) \\(\frac{1}{50}\\)
(b) \\(\frac{2}{15}\\)
(c) \\(\frac{3}{20}\\)
(d) \\(\frac{17}{60}\\)

Explanation:

Calculate the total number of surveys

Using the Theoretical Probability knowledge point

$$ \text{Total Surveys} = 9 + 18 + 22 + 8 + 3 = 60 $$

Determine individual probabilities

Using the Theoretical Probability knowledge point

$$
LATEXBLOCK0
$$

Calculate the joint probability

Using the Independent Events and Probability Multiplication Rule knowledge points

$$ P(\text{four first, then one}) = P(\text{four}) \times P(\text{one}) = \frac{2}{15} \times \frac{3}{20} = \frac{6}{300} = \frac{1}{50} $$

Answer:

• (A) \(\frac{1}{50}\) (Correct answer)
• (B) \(\frac{2}{15}\)
• (C) \(\frac{3}{20}\)
• (D) \(\frac{17}{60}\)