Question 1198975: A frequency distribution for the ages of the 40 students (including
undergraduate and graduate students) in Dr. Chung’s Probability and Statistics
class is presented in the Table below.
Age (yr)- Frequency
17 - 1
18 - 1
19 - 9
20 - 7
21 - 7
22 - 5
23 - 3
24 - 4
26 - 1
35 - 1
36 - 1
One student is selected at random. Let
A = event the student selected is under 21,
B = event the student selected is over 30,
C = event the student selected is in his or her 20s, and
D = event the student selected is over 18.
Determine probabilities of the following events:
a) (not D) b) (A & D) c) (A or D) d) (B or C)
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! **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
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