Question 1198975
**1. Calculate Total Frequency:**

* Total number of students = 1 + 1 + 9 + 7 + 7 + 5 + 3 + 4 + 1 + 1 + 1 = 40

**2. Define Events:**

* **A:** Student is under 21 (Age <= 20)
* **B:** Student is over 30 (Age > 30)
* **C:** Student is in their 20s (Age 20-29)
* **D:** Student is over 18 (Age > 18)

**3. Calculate Probabilities:**

* **P(A):** Probability of student being under 21
    * P(A) = (1 + 1 + 9 + 7) / 40 = 18/40 = 0.45

* **P(B):** Probability of student being over 30
    * P(B) = (1 + 1) / 40 = 2/40 = 0.05

* **P(C):** Probability of student being in their 20s
    * P(C) = (7 + 7 + 5 + 3 + 4) / 40 = 26/40 = 0.65

* **P(D):** Probability of student being over 18
    * P(D) = (9 + 7 + 7 + 5 + 3 + 4 + 1 + 1 + 1) / 40 = 38/40 = 0.95

**4. Calculate Probabilities of Compound Events:**

* **a) P(not D):** Probability of student not being over 18 (i.e., 18 or younger)
    * P(not D) = 1 - P(D) = 1 - 0.95 = 0.05

* **b) P(A & D):** Probability of student being under 21 and over 18 (i.e., 19 or 20)
    * P(A & D) = (9 + 7) / 40 = 16/40 = 0.4

* **c) P(A or D):** Probability of student being under 21 or over 18 (includes all students except those aged 17 or 18)
    * P(A or D) = P(A) + P(D) - P(A & D) = 0.45 + 0.95 - 0.4 = 1

* **d) P(B or C):** Probability of student being over 30 or in their 20s (includes all students except those under 20)
    * P(B or C) = P(B) + P(C) = 0.05 + 0.65 = 0.7

**In summary:**

* a) P(not D) = 0.05
* b) P(A & D) = 0.4
* c) P(A or D) = 1
* d) P(B or C) = 0.7