2. A survey is being conducted of students’ residences. Data is gathered from a random sample of 1000 students. The data is summarized in the table below. Gender and Residence of Students Males Females Apartment off campus 50 90 Dorm room 150 210 With Parent(s) 100 50 Sorority/ Fraternity House 200 150 a) What is the probability that a student is female and lives in a dorm? b) What is the probability that a student is female given that she lives in a dorm?

Gender and Residence of Students

a) What is the probability that a student is female and lives in a dorm?  

= 58.33%

b) What is the probability that a student is female given that she lives in a dorm?

= 21%

Step-by-step explanation:

a) Data and Calculations:

Gender and Residence of Students  

                                           Males   Females Total

Apartment off campus         50        90        140

Dorm room                          150       210       360

With Parent(s)                      100        50        150

Sorority/ Fraternity House 200      150        350

Total                                    500     500      1,000

a) Probability that a student is female and lives in a dorm:

= number of females who live in a dorm divided by total number of students who live in a dorm * 100

= 210/360 * 100

= 58.33%

b) Probability that a student is female given that she lives in a dorm

= number of female students who live in a dorm divided by the total number of students * 100

= 210/1,000 * 100

= 21%