In a management training program, 70% of the trainees are female and 30% male. 90% of the females attended college and 82% of the males attended college. (a) Draw a probability tree diagram showing all the possible outcomes (sample space) conditional probabilities, and joint probabilities. Round all probabilities to 3 decimal places if required. (b) Show that all the joint probabilities total to 1.000 (c) If one trainee was selected at random, what is the probability the selection would be a female that did attend college? Give your answer as a percent number. (d) If one trainee was selected at random, what is the probability the selection would be a male that did not attend college? Give your answer as a percent to one decimal place.