all freshmen, sophomores, juniors, and seniors attended a high school assembly. the total student attendance…

all freshmen, sophomores, juniors, and seniors attended a high school assembly. the total student attendance is shown in the table.\n| class | number of people |\n| ---- | ---- |\n| freshmen | 31 |\n| sophomores | 10 |\n| juniors | 17 |\n| seniors | 22 |\ntwice 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?\no $\frac{11}{320}$\no $\frac{3}{80}$\no $\frac{11}{40}$\no $\frac{2}{5}$

all freshmen, sophomores, juniors, and seniors attended a high school assembly. the total student attendance is shown in the table.\n| class | number of people |\n| ---- | ---- |\n| freshmen | 31 |\n| sophomores | 10 |\n| juniors | 17 |\n| seniors | 22 |\ntwice 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?\no $\frac{11}{320}$\no $\frac{3}{80}$\no $\frac{11}{40}$\no $\frac{2}{5}$

Answer

Explanation:

Step1: Calculate total number of students

$31 + 10+17 + 22=80$

Step2: Calculate probability of choosing a senior first

The number of seniors is 22. The probability $P(\text{senior first})$ is $\frac{22}{80}$.

Step3: Calculate probability of choosing a sophomore second

The number of sophomores is 10. Since the first - chosen student is replaced, the probability $P(\text{sophomore second})$ is $\frac{10}{80}$.

Step4: Calculate the combined probability

Since the two events are independent, we multiply the probabilities. $P = \frac{22}{80}\times\frac{10}{80}=\frac{22\times10}{80\times80}=\frac{220}{6400}=\frac{11}{320}$

Answer:

$\frac{11}{320}$