Question

Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.

NEXT QUESTION:


Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.

a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?

Please explain each step to me thank you

Answer 1

Given:
75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. → 25% goes to other schools.

five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. → 7% of the 5-star recruits don't get full football scholarships.

a. The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship? 
75% * 93% = 69.75%

b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?
25% of selected five-star recruit will not select a university from one of the three best conferences. I got the number based on the given data. Since, 75% will go, the remaining percent won't go. Total percentage should be 100% of the population. 

c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? 
These are independent events. One can still go to different school and still be legible for the full football scholarship. 

For question 2, pls. see attachment.