a private university is accepting applications for enrollment. out of 2,000 applicants, 950 meet the gpa…

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 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 mutually exclusive. thus, the probability is 65%. because some applicants volunteer and meet the gpa requirements, the events are not mutually exclusive. thus, the probability is 65%.

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 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 mutually exclusive. thus, the probability is 65%. because some applicants volunteer and meet the gpa requirements, the events are not mutually exclusive. thus, the probability is 65%.

Answer

Explanation:

Step1: Recall probability - addition formula

For non - mutually exclusive events (A) and (B), (P(A\cup B)=P(A)+P(B)-P(A\cap B)). Let (A) be the event that an applicant meets the GPA requirements and (B) be the event that an applicant volunteers. We know (n = 2000), (n(A)=950), (n(B)=600), (n(A\cap B)=250).

Step2: Calculate probabilities of individual and intersection events

(P(A)=\frac{n(A)}{n}=\frac{950}{2000}), (P(B)=\frac{n(B)}{n}=\frac{600}{2000}), (P(A\cap B)=\frac{n(A\cap B)}{n}=\frac{250}{2000}).

Step3: Calculate (P(A\cup B))

[ \begin{align*} P(A\cup B)&=\frac{950}{2000}+\frac{600}{2000}-\frac{250}{2000}\ &=\frac{950 + 600-250}{2000}\ &=\frac{1300}{2000}\ &=0.65 = 65% \end{align*} ] Since (n(A\cap B)=250\neq0), the events are not mutually exclusive.

Answer:

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