Question

all freshmen, sophomores, juniors, and seniors attended a high school assembly. the total student attendance is shown in the table.

\

$$\begin{tabular}{|c|c|} \\hline class & number of people \\\\ \\hline freshmen & 31 \\\\ \\hline sophomores & 10 \\\\ \\hline juniors & 17 \\\\ \\hline seniors & 22 \\\\ \\hline \\end{tabular}$$

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?

\\(\bigcirc \frac{11}{320}\\)
\\(\bigcirc \frac{3}{80}\\)
\\(\bigcirc \frac{11}{40}\\)
\\(\bigcirc \frac{2}{5}\\)

Explanation:

Calculate the total number of students

Using the Theoretical Probability knowledge point

$$ \text{Total students} = 31 + 10 + 17 + 22 = 80 $$

Determine the individual probabilities

Using the Theoretical Probability knowledge point

$$
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$$

Calculate the joint probability of independent events

Using the Independent Events and Probability Multiplication Rule knowledge points

$$ P(\text{Senior first and Sophomore second}) = P(\text{Senior}) \times P(\text{Sophomore}) = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320} $$

Answer:

• (A) \(\frac{11}{320}\) (Correct answer)
• (B) \(\frac{3}{80}\)
• (C) \(\frac{11}{40}\)
• (D) \(\frac{2}{5}\)