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

students in a class were surveyed about the number of children in their families. the results of the survey are shown in the table.\n\n| number of children in family | number of surveys |\n| ---- | ---- |\n| one | 9 |\n| two | 18 |\n| three | 22 |\n| four | 8 |\n| five or more | 3 |\n\ntwo 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?\n\no $\frac{1}{50}$\no $\frac{2}{15}$\no $\frac{3}{20}$\no $\frac{17}{60}$

students in a class were surveyed about the number of children in their families. the results of the survey are shown in the table.\n\n| number of children in family | number of surveys |\n| ---- | ---- |\n| one | 9 |\n| two | 18 |\n| three | 22 |\n| four | 8 |\n| five or more | 3 |\n\ntwo 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?\n\no $\frac{1}{50}$\no $\frac{2}{15}$\no $\frac{3}{20}$\no $\frac{17}{60}$

Answer

Explanation:

Step1: Calculate total number of surveys

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 in the family is $P_1=\frac{8}{60}$ since there are 8 surveys with four - children families out of 60 total surveys.

Step3: Calculate probability of second - survey result

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

Step4: Calculate combined probability

Since the two events are independent (because the first survey is returned), the probability of both events occurring is $P = P_1\times P_2=\frac{8}{60}\times\frac{9}{60}=\frac{72}{3600}=\frac{1}{50}$

Answer:

$\frac{1}{50}$