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. 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?\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|\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. 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?\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|\no $\frac{1}{50}$\no $\frac{2}{15}$\no $\frac{3}{20}$\no $\frac{17}{60}$

Answer

Explanation:

Step1: Calcular el total de encuestas

Sumamos el número de encuestas de cada categoría: $9 + 18+22 + 8+3=60$.

Step2: Calcular la probabilidad del primer evento

La probabilidad de que la primera encuesta indique cuatro hijos en la familia es $\frac{8}{60}$, ya que hay 8 encuestas que indican cuatro hijos y un total de 60 encuestas.

Step3: Calcular la probabilidad del segundo evento

La probabilidad de que la segunda encuesta indique un hijo en la familia es $\frac{9}{60}$, ya que hay 9 encuestas que indican un hijo y un total de 60 encuestas.

Step4: Calcular la probabilidad combinada

Como los eventos son independientes (ya que la primera encuesta se devuelve), multiplicamos las probabilidades: $\frac{8}{60}\times\frac{9}{60}=\frac{72}{3600}=\frac{1}{50}$.

Answer:

$\frac{1}{50}$