Question

75 points All freshmen, sophomores, juniors, and seniors attended a high school assembly. The total student attendance is shown in the table. 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?
a. 11/320
b. 3/80
c. 11/40
d. 2/5

Answer 1

Answer:- A is the right answer .

Probability that the first student chosen is a senior and the second student chosen is a sophomore=$\frac{11}{320}$

Explanation:-

According to the given table,

Total students=31+10+17+22= 80

Number of senior students = 22

Let A be the event 1 of choosing first student a senior

Then Probability of choosing first student a senior P(A) =$\frac{number\ of\ senior\ students}{total\ students}=\frac{22}{80}=\frac{11}{40}$

Now, Number of sophomores = 10

Let B be the event 2 of choosing second student a sophomore after replacing first student.

Then Probability of choosing second student a sophomore P(B)=$\frac{number\ of\ sophomores}{total\ students}=\frac{10}{80}=\frac{1}{8}$

As it is an independent event, then probability that the first student chosen is a senior and the second student chosen is a sophomore=P(A)×P(B)=$\frac{11}{40}\times\frac{1}{8}=\frac{11}{320}$

Answer 2

The answer is A. 11/320. Hope this helps.