there are 16 junior high students in the brewster town swimming club. a student is chosen at random to be…

there are 16 junior high students in the brewster town swimming club. a student is chosen at random to be the club vice - president.\nthe probability of choosing a 7th, 8th, or 9th grader is 1.\nthe probability of choosing a 7th grader is $\frac{1}{2}$.\nchoosing an 8th grader is more likely than choosing a 9th grader.\nwhat is the greatest possible number of 9th graders in the club?\n3\nthe probability of choosing a 9th grader is greater than 0. what is the least possible number of 9th graders in the club?

there are 16 junior high students in the brewster town swimming club. a student is chosen at random to be the club vice - president.\nthe probability of choosing a 7th, 8th, or 9th grader is 1.\nthe probability of choosing a 7th grader is $\frac{1}{2}$.\nchoosing an 8th grader is more likely than choosing a 9th grader.\nwhat is the greatest possible number of 9th graders in the club?\n3\nthe probability of choosing a 9th grader is greater than 0. what is the least possible number of 9th graders in the club?

Answer

Explanation:

Step1: Calcular el número de 7º graders

Dado que la probabilidad de elegir un 7º grader es $\frac{1}{2}$ y el total de estudiantes es 16, el número de 7º graders es $16\times\frac{1}{2}=8$.

Step2: Encontrar la cantidad de 8º y 9º graders

El total de 8º y 9º graders es $16 - 8=8$ ya que la probabilidad de elegir un 7º, 8º o 9º grader es 1.

Step3: Encontrar el máximo número de 9º graders

Como elegir un 8º grader es más probable que elegir un 9º grader, para maximizar el número de 9º graders, si el número de 9º graders es $x$, el número de 8º graders es $8 - x$ y $8 - x>x$. Resolviendo $8 - x>x$ da $2x<8$ o $x < 4$. Así, el máximo valor entero de $x$ es 3.

Step4: Encontrar el mínimo número de 9º graders

Dado que la probabilidad de elegir un 9º grader es mayor que 0, el mínimo número entero de 9º graders es 1.

Answer:

  1. 3
  2. 1