SOLUTION: 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 co

Question 1195764:
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.

Answer by ElectricPavlov(122) (Show Source): You can put this solution on YOUR website!
**a) Probability of a full scholarship for a recruit in a top conference:**
* Given:
* 75% of five-star recruits go to top three conferences.
* 93% of five-star recruits get full scholarships.
* Since the probability of getting a full scholarship is independent of the conference chosen (given in the problem), the probability of a five-star recruit in a top three conference getting a full scholarship is simply **93%**.
**b) Odds of a recruit NOT selecting a top three conference:**
* Probability of selecting a top three conference: 75%
* Probability of NOT selecting a top three conference: 100% - 75% = 25%
* Odds are typically expressed as a ratio of the probability of an event occurring to the probability of the event not occurring.
* Odds against selecting a top three conference:
* (Probability of NOT selecting) / (Probability of selecting)
* = 25% / 75%
* = 1/3
* Therefore, the odds of a randomly selected five-star recruit NOT selecting a university from one of the three best conferences are **1 to 3**.
**c) Independence and Inclusivity/Exclusivity:**
* **Independence:**
* The probability of a recruit getting a full scholarship is independent of the conference they choose. This is stated in the problem.
* **Inclusivity/Exclusivity:**
* The events "selecting a top three conference" and "not selecting a top three conference" are **mutually exclusive**. This means a recruit cannot simultaneously select a top three conference and not select a top three conference.
**In Summary:**
* a) Probability of a full scholarship for a recruit in a top conference: 93%
* b) Odds of a recruit NOT selecting a top three conference: 1 to 3
* c) Scholarship probability and conference choice are independent events.
* Selecting a top three conference and not selecting a top three conference are mutually exclusive events.

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