Chapter 3: Q.100 (page 226)

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 = the event that a student takes a distance learning class and E = the event that a student is a part-time student
a. Find P(D AND E).
b. Find P(E|D).
c. Find P(D OR E).
d. Using an appropriate test, show whether D and E are independent.
e. Using an appropriate test, show whether D and E are mutually exclusive.

Expert verified

a. P(D AND E) = $0.08$

b. P(E|D) = $0.8$

c. P(D OR E) = $0.42$

d. They are not independent

e. they are not mutually exclusive

Step by step solution

Mutually exclusive occasions are those that can't occur simultaneously, while independent are those whose probabilities don't influence each other.

Students who took distance-learning = $10 %$ or P(D) = role="math" localid="1651833127872" $0.1$

Students who are part-time = $40 %$ or P(E) = $0.4$

Part-time students who took distance-learning = $20 %$ or P(D/E) = $0.2$

D denote the distance learning classes event and E denotes a part-time event

$P (D a n d E) = P (D ∣ E) P (E)$

role="math" localid="1651897467873" $P (D a n d E) = 0.20 \times 0.40 = 0.08$

Students who took distance-learning = $10 %$ or P(D) = $0.1$

Students who are part-time = $40 %$ or P(E) = $0.4$

Part-time students who took distance-learning = $20 %$ or P(D/E) = $0.2$

$P (D and E) = 0.08$

$P (E ∣ D) = \frac{P (E a n d D)}{P (D)}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.