Question

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.

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?

A: Because some applicants volunteer and meet the GPA requirements, the events are mutually exclusive.Thus, the probability is 65%.

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

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

D: Because no applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 77.5%.

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Answer 1

Answer: Choice B

Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.

Thus, the probability is 65%.

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Step-by-step explanation:

950 people meet the GPA requirements. Also, 250 both meet the GPA requirements and volunteer. This must mean 950-250 = 700 people only meet the GPA requirements, but don't volunteer. Let A = 700.

600 people volunteer. 250 both meet the GPA requirements and volunteer. This must mean 600-250 = 350 people volunteer only (ie they don't meet the GPA requirements). Let B = 350

Let C = 250 to represent the number who meet the GPA requirements and volunteer.

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In summary we found that,

• A = 700 people meet the GPA requirements only (they don't volunteer)
• B = 350 people volunteer only (they don't meet the GPA requirements)
• C = 250 people both meet the GPA requirements and volunteer

That means A+B+C = 700+350+250 = 1300 people either meet the GPA requirements, volunteer, or both. This is out of 2000 people

1300/2000 = 13/20 = 0.65 = 65%

That calculation tells us that 65% of the 2000 applicants fit the conditions we're after. So that's the probability of randomly selecting someone to fit those conditions.

Because the value of C is not zero, this means we don't have mutually exclusive events. It's possible that someone fits both criteria. Mutually exclusive events cannot happen at the same time.

In other words, if we did have mutually exclusive events, then someone couldn't both meet the GPA requirements and volunteer at the same time (they would have to pick one or the other but not both).

Answer 2

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

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