A survey suggests that 65%, 60%, and 55% ofIEstudents indicated that they like Operations Research (OR), Production and Operations Management (POM), and Ergonomics (Ergo), respectively. Around 35%, 40%, and 25%, indicated that they like both OR and POM, OR and Ergo, and POM and Ergo, respectively. All students surveyed indicated that they like at least one of the three givenIEareas

1. Find the proportion of students who like all three areas. 2. Find the proportion of students who like OR alone. 3. What is the probability that a random student likes either POM or Ergo or both? 4. A random accomplished questionnaire indicated that the student likes OR. What is the probability that the same student likes POM as well? 5. Find the proportion of students who like exactly one area only.