Question

automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). the results are shown in the table below.

\

$$\begin{tabular}{|c|c|c|c|c|c|c|} \\hline & & \\multicolumn{4}{c|}{year in college} & \\\\ & & freshman & sophomore & junior & senior & total \\\\ \\hline \\multirow{2}{*}{car} & foreign & 15 & 65 & 100 & 25 & 205 \\\\ \\cline{2-7} & domestic & 10 & 45 & 80 & 10 & 145 \\\\ \\hline & total & 25 & 110 & 180 & 35 & 350 \\\\ \\hline \\end{tabular}$$

which of the following events listed would be considered mutually exclusive events?

• the student is a freshman and the student drives a foreign automobile
• the student is a senior and the student drives a domestic automobile
• the student is a junior and the student is a freshman
• the student is a junior and the student drives a domestic automobile

question 10 (1 point)
solve the problem.

fill in the blank. the ________ is the collection of all the sample points in an experiment.

Explanation:

Analyze the first question

Using the Two-Way Contingency Table knowledge point
We examine the contingency table to determine if the events can occur simultaneously. Two events \(A\) and \(B\) are mutually exclusive if they cannot happen at the same time, meaning \(P(A \cap B) = 0\).

• Option 1: "The student is a freshman and the student drives a foreign automobile." From the table, there are 15 students who are both freshmen and drive foreign cars. Since \(15 > 0\), these are not mutually exclusive.
• Option 2: "The student is a senior and the student drives a domestic automobile." There are 10 students who are seniors and drive domestic cars. Since \(10 > 0\), these are not mutually exclusive.
• Option 3: "The student is a junior and the student is a freshman." A student can only be classified in one college year (freshman, sophomore, junior, or senior) at a time. The intersection of being a junior and a freshman is 0. Thus, these are mutually exclusive.
• Option 4: "The student is a junior and the student drives a domestic automobile." There are 80 students who are juniors and drive domestic cars. Since \(80 > 0\), these are not mutually exclusive.

Analyze the second question

We define the fundamental terminology of probability experiments.
The collection of all possible outcomes or sample points of a random experiment is defined as the sample space.
Therefore, the term that fills the blank is "sample space".

Answer:

Question 1

• (A) The student is a freshman and the student drives a foreign automobile
• (B) The student is a senior and the student drives a domestic automobile.
• (C) The student is a junior and the student is a freshman (Correct answer)
• (D) The student is a junior and the student drives a domestic automobile

Question 2

Fill in the blank. The <blank>sample space</blank> is the collection of all the sample points in an experiment.