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

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

Answer

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 $\frac{8}{60}$ since there are 8 surveys with four children out of 60 total surveys.

Step3: Calculate probability of second - survey result

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

Step4: Calculate combined probability

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

Answer:

$\frac{1}{50}$