In a management trainee program at Claremont Enterprises, 80% of the trainees are female and 20% male. Ninety percent of the females attended college, and 78% of the males at-tended college.,a. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college?,b. Are gender and attending college independent? Why?,c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities.,d. Do the joint probabilities total 1.00? Why?