Question

all freshmen, sophomores, juniors, and seniors attended a high school assembly. the total student attendance is shown in the table.

class	number of people
sophomores	10
juniors	17
seniors	22

twice during the assembly, a student is chosen at random to assist with the presentation. after the first student has finished assisting, the student returns to the group and can be chosen a second time. what is the probability that the first student chosen is a senior and the second student chosen is a sophomore?
o $\frac{11}{320}$
o $\frac{3}{80}$
o $\frac{11}{40}$
o $\frac{2}{5}$

Explanation:

Step1: Calcular el total de estudiantes

$31 + 10+17 + 22=80$

Step2: Calcular la probabilidad de elegir un senior primero

La probabilidad de elegir un senior primero es $\frac{22}{80}$ ya que hay 22 seniors y 80 estudiantes en total.

Step3: Calcular la probabilidad de elegir un sophomore segundo

Como el primer estudiante regresa al grupo, la probabilidad de elegir un sophomore segundo es $\frac{10}{80}$ ya que hay 10 sophomores y 80 estudiantes en total.

Step4: Calcular la probabilidad conjunta

La probabilidad de que el primer estudiante sea un senior y el segundo un sophomore es el producto de las dos probabilidades: $\frac{22}{80}\times\frac{10}{80}=\frac{22\times10}{80\times80}=\frac{220}{6400}=\frac{11}{320}$

Answer:

A. $\frac{11}{320}$