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.

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

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

Explanation:

Step1: Calculate total number of surveys

Add up the number of surveys in each category: $9 + 18+22 + 8+3=60$.

Step2: Calculate probability of first - event

The probability that the first survey indicates four children is the number of surveys with four children divided by the total number of surveys. So $P(\text{first - four})=\frac{8}{60}$.

Step3: Calculate probability of second - event

The probability that the second survey indicates one child is the number of surveys with one child divided by the total number of surveys. So $P(\text{second - one})=\frac{9}{60}$.

Step4: Calculate joint probability

Since the two events are independent (because the first survey is returned), the joint probability is the product of the two probabilities. $P = \frac{8}{60}\times\frac{9}{60}=\frac{72}{3600}=\frac{1}{50}$.

Answer:

$\frac{1}{50}$