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. If this pattern holds true for this year’s recruiting class, answer the following:
REST OF QUESTION IN COMMENTS

Answer 1

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 2

would you like help with this?

Answer 3

Yes please @perl

Answer 4

i need to leave right now, emergency, i will be back in 5 minutes, is that ok?

Answer 5

this is all the information given, correct?

Answer 6

yeah that's it @perl

Answer 7

I think I know the answe to b and c but I have no idea for a. Here are my answers so far:
a)
b) The odds against a five-star football recruit going to a university from one of the three best conferences is 1:3, because since they have a 3/4 probability of going to one, there is 1 to 3 odds against
c) This is an inclusive event because a five-star football player could go to one of the universities in the three most athletic conferences and have a full football scholarship at the same time. It is also a dependent event, because if you don't go to a university or college, then you can't get a scholarship.
@perl

Answer 8

it would also help to define these terms
what is a five star football recruit?

Answer 9

I think it means someone who is extremely good at football and is playing football as a career?

Answer 10

i think it means that a student is recruited from high school by a college athletic coach

Answer 11

Oh okay

Answer 12

for part a) , lets do it this way.
Let A = five start recruit goes to university in one of three most competitive athletic conferences
B = five star recruit gets full football scholarship

we want to know P( A & B )

P(A & B ) = P( A ) * P(B) = .75 * .93

Answer 13

i presume that a 5 star college football recruit has his choice of college . the five star means he has the highest rating

Answer 14

Wait, so does that mean that this is an independent event? I thought this was a dependent event, because you can't get a scholarship if you don't go to a college

Answer 15

i see what youre saying, but i dont see any other way to solve this , but by treating the events as independent

Answer 16

My course says that to find the probability of a dependent event is:
P( A and B) = P(A) * (B following A). But I don't know how to find the "B following A" part

Answer 17

you have to understand that all the athletic colleges know about the five star recruits, they are nationally known. so they offer scholarships to these high school students, even if they don't commit to going to college.

Answer 18

these athletes are highest ranked in the country, so they get to choose which athletic college they want to go to.
And colleges pre-offer scholarships to the five star recruit athletes

Answer 19

Ohhhh that makes a lot more sense, so in that case, this is an independent event right?

Answer 20

so here P(B | A ) = P(B)

Answer 21

here is an example http://ukrecruiting.bloginky.com/2015/05/19/calipari-offers-scholarship-to-another-five-star-recruit/

Answer 22

I got about 69.75% for the answer to a, is that right?

Answer 23

correct

Answer 24

Okay thank you so much! You're very helpful!

Answer 25

they are independent , because all the athletic colleges are willing to offer these five star recruits scholarships , regardless of where the athlete makes his final pick. of course the college cannot read his mind before he makes his pick.

Answer 26

think of a scholarship as a way of a college saying, come to *my* school.

Answer 27

Actually, wouldn't the probability be higher, since in the original question a says that the football recruit will for sure be going to a college

Answer 28

colleges generate a lot of money from athletes

Answer 29

from the games, ticket sales, etc

Answer 30

the probability would be lower because you are multiplying probabilities

Answer 31

But the original problem says that for sure the football guy will be going to a university

Answer 32

we are asking about the probability of going to a university in the three most competitive athletic conference and being offered a full scholarship .

Answer 33

so you are talking about a select few colleges or a subset of colleges, the three most competitive atheletic conference college (whatever that means)

Answer 34

that article i posted gives you an example of an early scholarship offer

`The 6-foot-10 prospect from Austin is considered by Scout.com to be the No. 15 overall prospect in the class of 2016. Kansas, Texas and Baylor also have extended early scholarship offers.`
http://ukrecruiting.bloginky.com/2015/05/19/calipari-offers-scholarship-to-another-five-star-recruit/

Answer 35

75% of five star recruits end up going to the three most athletic conference college. and 93% of five star recruits get a full scholarship, regardless of the athletic college they go to (whether its in the three most athletic conference or not).