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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.

Short Answer

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

01

introduction

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

02

explanation part (a)

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(DandE)=P(D鈭�E)P(E)

role="math" localid="1651897467873" P(DandE)=0.20脳0.40=0.08

03

explanation part (b)

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(DandE)=0.08

P(E鈭�D)=P(EandD)P(D)

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