Female business majors: At a certain university, the probability that a randomly chosen student is female is 0.55, the probability that the student is a business major is 0.20, and the probability that the student is female and a business major is 0.15.
a. What is the probability that the student is female or a business major?
b. What is the probability that the student is female given that the student is a business major?
c. What is the probability that the student is a business major given that the student is female?
d. Are the events ‘‘female’’ and ‘‘business major’’ independent? Explain.
e. Are the events ‘‘female’’ and ‘‘business major’’ mutually exclusive? Explain.