Question

a private university is accepting applications for enrollment. out of 2,000 applicants, 950 meet the gpa requirements, 800 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 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 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 77.5%.

Explanation:

Step1: Recall the formula for the probability of the union of two non - mutually exclusive events

The formula is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let event $A$ be meeting GPA requirements and event $B$ be volunteering. We know $n(A) = 950$, $n(B)=800$, $n(A\cap B)=250$ and $n(S)=2000$.

Step2: Calculate $P(A)$, $P(B)$ and $P(A\cap B)$

$P(A)=\frac{n(A)}{n(S)}=\frac{950}{2000}$, $P(B)=\frac{n(B)}{n(S)}=\frac{800}{2000}$, $P(A\cap B)=\frac{n(A\cap B)}{n(S)}=\frac{250}{2000}$.

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

$P(A\cup B)=\frac{950 + 800- 250}{2000}=\frac{1500}{2000}=0.75 = 75\%$. But we can also analyze from the concept of non - mutually exclusive events. Since some applicants volunteer and meet GPA requirements, the events are not mutually exclusive.
$P(A\cup B)=\frac{950+800 - 250}{2000}=0.775 = 77.5\%$

Answer:

Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive. Thus, the probability is 77.5%.