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?
○ $\frac{11}{320}$
○ $\frac{3}{80}$
○ $\frac{11}{40}$
○ $\frac{2}{5}$

Explanation:

Step1: Calculate total number of students

$31 + 10+17 + 22=80$

Step2: Calculate probability of first - student being a senior

The probability $P(\text{senior})$ that the first student chosen is a senior is $\frac{22}{80}$ since there are 22 seniors out of 80 total students.

Step3: Calculate probability of second - student being a sophomore

Since the first student is replaced, the probability $P(\text{sophomore})$ that the second student chosen is a sophomore is $\frac{10}{80}$ as there are 10 sophomores out of 80 total students.

Step4: Calculate the combined probability

Since these are independent events, the probability that the first student is a senior and the second is a sophomore is $P = \frac{22}{80}\times\frac{10}{80}=\frac{220}{6400}=\frac{11}{320}$

Answer:

$\frac{11}{320}$