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. 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?

number of children in family	number of surveys
two	18
three	22
four	8
five or more	3

o $\frac{1}{50}$
o $\frac{2}{15}$
o $\frac{3}{20}$
o $\frac{17}{60}$

Explanation:

Answer:

First, find the total number of surveys: \(9 + 18+22 + 8+3=60\).
The probability that the first - survey indicates four children is \(\frac{8}{60}\), and the probability that the second survey indicates one child is \(\frac{9}{60}\).
Since the events are independent (because the first survey is returned), the probability of both events occurring is the product of their probabilities.
\(P=\frac{8}{60}\times\frac{9}{60}=\frac{72}{3600}=\frac{1}{50}\)
So the answer is \(\frac{1}{50}\)