To answer the questions, we first need to calculate the total number of students and then use this to calculate probabilities.
Total Number of Students
Let's add up the number of students in each GPA range:
- 1.00 - 1.49: 5
- 1.50 - 1.99: 13
- 2.00 - 2.49: 20
- 2.50 - 2.99: 27
- 3.00 - 3.49: 25
- 3.50 - 4.00: 7
Total = 5 + 13 + 20 + 27 + 25 + 7 = 97 students
Question 1
We want to find the probability that a student has a GPA between 3.00 - 3.49 OR between 3.50 - 4.00.
Number of students in each GPA range:
- 3.00 - 3.49: 25
- 3.50 - 4.00: 7
Total number of students in the specified ranges: 25 + 7 = 32 students
Now, we can find the probability: \[ P(\text{GPA between 3.00 - 3.49 or 3.50 - 4.00}) = \frac{\text{Number of students in these ranges}}{\text{Total number of students}} = \frac{32}{97} \]
Thus, the probability is \( \frac{32}{97} \).
Question 2
The complement of the event in Question 1 is that a student does not have a GPA between 3.00 - 3.49 or between 3.50 - 4.00.
In words, the complement is:
- "A student has a GPA less than 3.00 or greater than 4.00."
To find the probability of this complement event:
- First, calculate the number of students not in the specified GPA ranges:
- Total students = 97
- Students with GPA between 3.00 - 4.00 = 32
- Students not in these ranges = 97 - 32 = 65 students
Now, we can find the probability of the complement: \[ P(\text{Not GPA between 3.00 - 3.49 or 3.50 - 4.00}) = \frac{\text{Number of students not in these ranges}}{\text{Total number of students}} = \frac{65}{97} \]
Thus, the probability of the complement is \( \frac{65}{97} \).
Summary
- Probability of having a GPA between 3.00 - 3.49 or 3.50 - 4.00: \( \frac{32}{97} \)
- Complement: "A student has a GPA less than 3.00 or greater than 4.00." Probability of the complement: \( \frac{65}{97} \)
1 answer