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.

Answer 1

The problem above can be shown on a tree diagram as shown below

Question a)

Let C represents the five-star recruit who chooses one of the best three conferences
Let S represents the scholarship offer

P(C∩S) = 0.75×0.93 = 0.6975

Question b)

P(C'∩S) = 0.75×0.07 = 0.0525

Question c)

The two events are independent because it is possible for the events to happen in any order and one event's outcome does not affect the other event's.