A private university is accepting applications for enrollment. Out of 2000 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 opplicants 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%. 

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

A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth. 

A security alarm requires a four-digit code. The code can use the digits \(0 - 9\) and the digits cannot be repeated. 

What is the approximate probability that the code only contains odd numbers? 

0.0005

0.00099

0.012

0.02381

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below: 

Spinner Results

Color Frequency

Red   7

Blue  15

Green  6

Yellow  5

Purple  8

Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth. 

g. A ball is drawn from a box containing \(4\) red balls, \(7\) green balls and \(8\) blue balls. Find the probability that the ball drawn is 

i) red                     iii) blue 

ii) red or green      iv) not blue 

Determine whether events "drawing a red ball" and "drawing a blue ball" are mutually exclusive?