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.