3:28 class.daytonastate.edu If we add up the numbers, we see they sum to 156. This means there are 165 - 156 = 9 students not taking any of the three courses. Part 2: Calculating Probabilities Problem 2 Problem Statement The local college had 578 new students register for courses this semester. Many of the students enrolled into one or more courses from the humanities, science, business, or math departments as shown in the Venn Diagram here. Humanities Science 53 80 33 13 31 25 45 28 66 55 Business Math Questions 1. Based on the current data, what department has the highest probability of "new student enrollment?" Give your answers as a fraction in lowest terms. What is the probability a new student enrolls into a humanities course? b. What is the probability a new student enrolls into a science course? c. What is the probability a new student enrolls into a math course? d. What is the probability a new student enrolls into a business course? e. Which of the four departments has the highest probability of "new student enrollment?" 2. Based on the current data, what is the probability a new student enrolled in a science course is also enrolled in a math course? Give your answer as a fraction in lowest terms. 3. Based on the current data, what is the probability a new student enrolled in a science course is also enrolled in a math and humanities course? Give your answer as a fraction in lowest terms. 4. Based on the current data, which department has the highest probability of students enrolled in one of their courses only? Give your answer as a fraction in lowest terms. a. What is the probability a new student enrolled in a math course is enrolled only in a math course? What is the probability a new student enrolled in a business course is enrolled only in a business course? C. What is the probability a new student enrolled in a science course is enrolled only in a science course? What is the probability a new student enrolled in a humanities course is enrolled only in a humanities course? e. Which department has the highest probability of students enrolled in one of their courses only? 5. If the current data is an accurate predictor of future new student enrollment, how many students should the college expect to enroll into a course from all four departments if 900 new students enroll next semester? What is the probability a new student will enroll into a course from all four departments? Give your answer as a fraction in lowest terms. b. How many students should the college expect to enroll into a course from all four department if 900 new students enroll next semester? Give your answer as a whole number. Example