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 no applicants volunteer and meet the gpa requirements, the events are 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%.

Explanation:

Step1: Calculate probability of meeting GPA

Probability of meeting GPA = $\frac{950}{2000}= 0.475$ or 47.5%

Step2: Calculate probability of being volunteer

Probability of being volunteer = $\frac{600}{2000}=0.3$ or 30%

Step3: Calculate probability of both

Since events are not mutually - exclusive, probability of both = $\frac{250}{2000}=0.125$ or 12.5%

Step4: Use addition rule for non - mutually exclusive events

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$P(A\cup B)=0.475 + 0.3-0.125=0.65$ or 65%

Answer:

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