Question

1. - / 5 points a college finds that 10% of students have taken a distance learning class and that 40% of students are part - time students. of the part - time students, 20% have taken a distance learning class. let d = event that a student takes a distance learning class and e = event that a student is a part - time student. part (a) find p(d and e) part (b) part (c) part (d) part (e) resources reading

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \( P(D|E) = \frac{P(D \cap E)}{P(E)} \), which can be rearranged to find \( P(D \cap E) \) (which is \( P(D \text{ AND } E) \)) as \( P(D \cap E) = P(D|E) \times P(E) \).

Step2: Identify the given probabilities

We know that \( P(E) = 0.40 \) (since 40% of students are part - time students) and \( P(D|E)=0.20 \) (since 20% of part - time students have taken a distance learning class).

Step3: Calculate \( P(D \text{ AND } E) \)

Substitute the values into the formula: \( P(D \text{ AND } E)=P(D|E)\times P(E)=0.20\times0.40 = 0.08 \)

Answer:

\( 0.08 \)