Qualifying exam | Mathematics homework help

Use the following results: In the judicial case of United States v. City of Chicago, discrimination was charged in a qualifying exam for the position of Fire Captain. In the table below, Group A is a minority group and Group B is a majority group.

 

Passed

Failed

Group A

10

14

Group B

417

145

a) If one of the test subjects is randomly selected, find the probability of getting someone who passed the exam.
b) Find the probability of randomly selecting one of the test subjects and getting someone who is in Group B or passed.
c) Find the probability of randomly selecting two different test subjects and finding that they are both in Group A.
d) Find the probability of randomly selecting one of the test subjects and getting someone who is in Group A and passed the exam.
e) Find the probability of getting someone who passed, given that the selected person is in Group A.