Question

a private university is accepting applications for enrollment. out of 2,000 applicants, 950 meet the gpa requirements, 600 volunteer for community service, and 250 both meet the gpa requirements and volunteer. which statement correctly describes the probability that an applicant meets the gpa requirements or volunteers? because some applicants volunteer and meet the gpa requirements, the events are not mutually exclusive. thus, the probability is 77.5%. because some applicants volunteer and meet the gpa requirements, the events are not mutually exclusive. thus, the probability is 65%. because some applicants volunteer and meet the gpa requirements, the events are mutually exclusive. thus, the probability is 65%. because no applicants volunteer and meet the gpa requirements, the events are mutually exclusive. thus, the probability is 77.5%.

Explanation:

Step1: Identify total and favorable cases

Total number of applicants $n = 2000$. Number of applicants who meet GPA requirements $n_{GPA}=950$, number of applicants who are volunteers $n_{volunteer}=600$, and number of applicants who meet both $n_{both}=250$.

Step2: Use probability formula for non - mutually exclusive events

The probability of an applicant meeting GPA or being a volunteer is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $P(A)=\frac{n_{GPA}}{n}$, $P(B)=\frac{n_{volunteer}}{n}$, and $P(A\cap B)=\frac{n_{both}}{n}$.
$P(A)=\frac{950}{2000}=0.475$, $P(B)=\frac{600}{2000}=0.3$, $P(A\cap B)=\frac{250}{2000}=0.125$.
$P(A\cup B)=0.475 + 0.3-0.125=0.65$ or $65\%$. Since meeting GPA and being a volunteer are not mutually - exclusive events (as some applicants are in both categories), the correct statement is: Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive. Thus, the probability is $65\%$.

Answer:

Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive. Thus, the probability is $65\%$.