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

Explanation:

Step1: Calculate total number of surveys

$9 + 18+22 + 8+3=60$

Step2: Calculate probability of first - survey result

The probability that the first survey indicates four children is $P_1=\frac{8}{60}$ since there are 8 surveys with four - children response out of 60 total surveys.

Step3: Calculate probability of second - survey result

The probability that the second survey indicates one child is $P_2=\frac{9}{60}$ since there are 9 surveys with one - child response out of 60 total surveys.

Step4: Calculate joint probability

Since the two surveys are independent (because the first survey is returned before the second draw), the joint probability $P = P_1\times P_2$.
$P=\frac{8}{60}\times\frac{9}{60}=\frac{72}{3600}=\frac{1}{50}$

Answer:

$\frac{1}{50}$