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?
$\frac{11}{320}$
$\frac{1}{80}$
$\frac{11}{40}$
$\frac{1}{5}$

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 $\frac{\text{Number of seniors}}{\text{Total number of students}}=\frac{22}{80}$

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 $\frac{\text{Number of sophomores}}{\text{Total number of students}}=\frac{10}{80}$

Step4: Calculate joint probability

Since the two events are independent (because of replacement), the probability that the first student is a senior and the second is a sophomore is $P = P(\text{senior})\times P(\text{sophomore})=\frac{22}{80}\times\frac{10}{80}=\frac{22\times10}{80\times80}=\frac{220}{6400}=\frac{11}{320}$

Answer:

$\frac{11}{320}$