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 probability that a five-star recruit will be offered a full football scholarship if they choose one of the top three conferences is 93%, while the odds of not selecting such a university are 25%.

These events are independent and exclusive as the choice of conference does not affect the likelihood of receiving a scholarship and recruits cannot simultaneously select and not select a top university.

Step-by-step explanation:

To solve these probabilities, we will use the given historical percentages.

1. The probability that a randomly selected five-star recruit who chooses one of the three most competitive athletic conferences will be offered a full football scholarship is just the probability of getting the scholarship, since the choice of conference does not affect scholarship offerings. This probability is 93%.
2. The odds a randomly selected five-star recruit will not select a university from one of the three best conferences are determined by subtracting the probability of selecting one of the top conferences (75%) from 100%. That gives us 25%, or a 1 in 4 chance.
3. These events are independent because the choice of conference does not affect the likelihood of receiving a scholarship. The events are exclusive because a recruit can either choose a university in one of the top three conferences or not (they cannot do both).

Answer 2

a. is an independent event so P(B | A ) = P(B) with the answer being 69.75%. That is all I've got so hope this helps a little.