Question

each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. the results are shown in the contingency table. find the probability that the student preferred morning classes given he or she is a freshman. round to the nearest thousandth.

when do you prefer to take classes?

\

$$\begin{tabular}{|c|c|c|c|c|} \\hline & freshman & sophomore & junior & senior \\\\ \\hline morning & 6 & 4 & 16 & 18 \\\\ \\hline afternoon & 7 & 7 & 10 & 11 \\\\ \\hline evening & 6 & 10 & 5 & 4 \\\\ \\hline \\end{tabular}$$

\bigcirc 0.316

\bigcirc 0.211

Explanation:

Identify the given condition and target event

Using the Conditional Probability knowledge point

$$
LATEXBLOCK0
$$

Calculate the total number of freshmen

Using the Conditional Probability knowledge point

$$
LATEXBLOCK1
$$

Find the number of freshmen preferring morning classes

Using the Conditional Probability knowledge point

$$ n(\text{Morning} \cap \text{Freshman}) = 6 $$

Compute the conditional probability

Using the Conditional Probability knowledge point

$$
LATEXBLOCK2
$$

Round to the nearest thousandth

Using the Conditional Probability knowledge point

$$ P(\text{Morning} \mid \text{Freshman}) \approx 0.316 $$

Answer:

• (A) 0.316 (Correct answer)
• (B) 0.211