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 freshmen 31 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? 11/320 3/80 11/40 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 $P_1$ that the first student chosen is a senior is the number of seniors divided by the total number of students. So $P_1=\frac{22}{80}=\frac{11}{40}$

Step3: Calculate probability of second - student being a sophomore

Since the first student is replaced, the total number of students remains the same. The probability $P_2$ that the second student chosen is a sophomore is the number of sophomores divided by the total number of students. So $P_2=\frac{10}{80}=\frac{1}{8}$

Step4: Calculate the joint - probability

Since the two events are independent (because the first student is replaced), the probability that the first student is a senior and the second student is a sophomore is $P = P_1\times P_2$.
$P=\frac{11}{40}\times\frac{1}{8}=\frac{11}{320}$

Answer:

$\frac{11}{320}$