4. A grade 12 student is selected at random to sit on a university committee. Of the 120 students enrolled in the grade 12 university-preparation mathematics courses,
* 28 are enrolled in data management only
* 40 are enrolled in calculus only
* 15 are enrolled in geometry only
* 16 are enrolled in both data management and calculus
* 12 are enrolled in both calculus and geometry
* 6 are enrolled in both geometry and data management
* 3 are enrolled in all three of data management, calculus and geometry
a) Draw a Venn diagram to illustrate this situation
(6 Marks)
b) Determine the probability that the student selected will be enrolled in either data management or calculus.
(3 Marks)
c) Determine the probability that the student selected will be enrolled in only one of the three courses.
(3 Marks)

Step 1 ：First, we need to find the number of students enrolled in each course and their intersections.

Step 2 ：Data Management: \(28 + 16 + 6 + 3 = 47\) students

Step 3 ：Calculus: \(40 + 16 + 12 + 3 = 65\) students

Step 4 ：Geometry: \(15 + 12 + 6 + 3 = 30\) students

Step 5 ：b) Determine the probability that the student selected will be enrolled in either data management or calculus.

Step 6 ：\(P(\text{Data Management or Calculus}) = \frac{\text{Data Management} + \text{Calculus} - \text{Both}}{\text{Total Students}}\)

Step 7 ：\(P(\text{Data Management or Calculus}) = \frac{47 + 65 - 16}{120} = \frac{96}{120} = 0.8\)

Step 8 ：\(\boxed{0.8}\)

Step 9 ：c) Determine the probability that the student selected will be enrolled in only one of the three courses.

Step 10 ：\(P(\text{Only One Course}) = \frac{\text{Data Management Only} + \text{Calculus Only} + \text{Geometry Only}}{\text{Total Students}}\)

Step 11 ：\(P(\text{Only One Course}) = \frac{28 + 40 + 15}{120} = \frac{83}{120} \approx 0.692\)

Step 12 ：\(\boxed{0.692}\)