The university's library has been randomly surveying patrons over the last month to see who is using the library and what services they have been using. Patrons are classified as undergraduate, graduate, or faculty. Services are classified as reference, periodicals, or books. The data for 350 people are given below. Assume a patron uses only one service per visit.

Patron

Reference

Periodicals

Books

Undergraduate

44

 26

 72

Graduate

24

 61

 20

Faculty

16

 69

 18

 

84

156

110

Find the probability that a randomly chosen patron

(a) Is a graduate student.

(b) Visited the periodicals section, given the patron is a graduate student.

(c) Is a faculty member, given a reference section visit.

(d) Is an undergraduate who visited the book section.

Answer:

The university's library has been randomly surveying patrons over the last month to see who is using the library and what services they have been using. 

The data for 350 people are given below.

Step-by-step explanation

The data for 350 people: 84+156+110=350

(a) Is a graduate student:

P( Is a graduate student) =total graduate/ Total people=105/350= 0.3

(b) Visited the periodicals section, given the patron is a graduate student:

P( The periodicals section/ the patron is a graduate student) = P( The periodicals section ? the patron is a graduate student) /P(graduate student)

P( The periodicals section/ the patron is a graduate student) = (61/350) / (105/350) = 0.5809

(c) Is a faculty member, given a reference section visit:

P(faculty member / reference section)=P(faculty member ?reference section)/ P( reference section)

P(faculty member / reference section)= (16/350) / (84/350) = 0.1904

(d) Is an undergraduate who visited the book section:

P( Is an undergraduate who visited the book section)= 72/350 = 0.2057

PFA